IMRAN SIDDIQUE

The concept of resolving sets (RSs) and metric dimension (MD) invariants have a wide range of applications in robot navigation, computer networks, and chemical structure. RS has been used as a sensor in an indoor positioning system to find an interrupter. Many terminologies in machine learning have also been used to diagnose the interrupter in the systems of marine and gas turbines using sensory data. We proposed a fault-tolerant self-stable system that allows for the detection of an interrupter even if one of the sensors in the chain fails. If the elimination of any element from a RS is still a RS, then the RS is considered as a fault-tolerant resolving set (FTRS), and the fault-tolerant metric dimension (FTMD) is its minimum cardinality. In this paper, we calculated the FTMD of the subdivision graphs of the necklace and prism graphs. We also found that this invariant has constant values for both graphs.

Topological indices are very useful to assume certain physiochemical properties of the chemical compound. A molecular descriptor which changes the molecular structures into certain real numbers is said to be a topological index. In chemical graph theory, to create quantitative structure activity relationships in which properties of molecule may be linked with their chemical structures relies greatly on topological indices. The benzene molecule is a common chemical shape in chemistry, physics, and nanoscience. This molecule could be very beneficial to synthesize fragrant compounds. The circumcoronene collection of benzenoid H m is one family that generates from benzene molecules. The purpose of this study is to calculate the topological indices of the double and strong double graphs of the circumcoronene series of benzenoids H m . In addition, we also present a numerical and graphical comparison of topological indices of the double and strong double graphs of the circumcoronene serie...

Toeplitz networks are used as interconnection networks due to their smaller diameter, symmetry, simpler routing, high connectivity, and reliability. The edge metric dimension of a network is recently introduced, and its applications can be seen in several areas including robot navigation, intelligent systems, network designing, and image processing. For a vertex s and an edge g = s 1 s 2 of a connected graph G , the minimum number from distances of s with s 1 and s 2 is called the distance between s and g . If for every two distinct edges s 1 , s 2 ∈ E G , there always exists w 1 ɛ W E ⊆ V G , such that d s 1 , w 1 ≠ d s 2 , w 1 ; then, W E is named as an edge metric generator. The minimum number of vertices in W E is known as the edge metric dimension of G . In this study, we consider four families of Toeplitz networks T n 1,2 , T n 1,3 , T n 1,4 , and T n 1,2,3 and studied their edge metric dimension. We prove that for all n ≥ 4 , e dim T n 1,2 = 4 , for n ≥ 5 , e dim T n 1,3 = 3 ...

Experts are using picture fuzzy sets (PFSs) in their probes to resolve the uncertain and vague information during the process of decision making because PFSs describe human attitudes naturally. Divergence measure (DM) plays a dominant role in discriminating between two distributions of probability and extracting consequences from that discrimination. In the present work, a novel picture fuzzy divergence measure (PF-DM) is developed between two PFSs. Some of the suggested measure’s important qualities are also discussed with particular situations to validate it. Based on the suggested PF-DM, a multiple-criteria decision-making (MCDM) model is established to grab the fuzzy information. The suggested measure’s performance is compared to that of various existing measures in the literature. An MCDM model has been proven for the usefulness of the suggested technique in dealing with real-life scenarios in the context of dengue sickness and pattern identification. Validation of the suggeste...

In this article, we explore how activation energy and varied transit parameters influence the two-dimensional stagnation point motion of nano-biofilm of Sutterby fluids incorporating gyrotactic microbes across a porous straining/shrinking sheet. Prior investigations implied that fluid viscosity as well as thermal conductance are temperature based. This research proposes that fluid viscosity, heat capacity and nanofluid attributes are all modified by solute concentration. According to some empirical research, the viscosity as well as heat conductivity of nanoparticles are highly based on the concentration of nanoparticles instead of only the temperature. The shooting approach with the RK-4 technique is applied to acquire analytical results. We contrast our outcomes with those in the existing research and examine their consistency and reliability. The graphic performance of relevant factors on heat, velocity, density and motile concentration domains are depicted and discussed. The ski...

In the current work, an investigation has been carried out for the Bingham fluid flow in a channel-driven cavity with a square obstacle installed near the inlet. A square cavity is placed in a channel to accomplish the desired results. The flow has been induced using a fully developed parabolic velocity at the inlet and Neumann condition at the outlet, with zero no-slip conditions given to the other boundaries. Three computational grids, C1, C2, and C3, are created by altering the position of an obstacle of square shape in the channel. Fundamental conservation and rheological law for viscoplastic Bingham fluids are enforced in mathematical modeling. Due to the complexity of the representative equations, an effective computing strategy based on the finite element approach is used. At an extra-fine level, a hybrid computational grid is created; a very refined level is used to obtain results with higher accuracy. The solution has been approximated using P2 − P1 elements based on the sh...

The present study especially concerns the investigation of the Couette flow and heat transfer with thermal radiation through an inclined channel. Single-wall carbon nanotube (SWCNT) and multiple-wall carbon nanotube (MWCNT) are nanoparticles embedded in the host fluid. The dimensionless highly nonlinear differential equations (DEs) are solved via numerical scheme bvp4c. The effects of the physical parameters on heat transfer are presented in the form of graphs. The results demonstrate that the heat transfer is enhanced by using solid particle frictions (SWCNT and MWCNT). The large estimation of a magnetic parameter declines the velocity component. The current and existing results with their comparisons are shown in the tabular form for the validation of our code. The current results are in good agreement with their existing results. Generally, fuzziness or uncertainty is inherent in modeling, analysis, and experimentation. Due to the uncertain environmental conditions, fuzziness bro...

The electrocardiogram (ECG) is one of the most widely used diagnostic instruments in medicine and healthcare. Deep learning methods have shown promise in healthcare prediction challenges involving ECG data. This paper aims to apply deep learning techniques on the publicly available dataset to classify arrhythmia. We have used two kinds of the dataset in our research paper. One dataset is the MIT-BIH arrhythmia database, with a sampling frequency of 125 Hz with 1,09,446 ECG beats. The classes included in this first dataset are N, S, V, F, and Q. The second database is PTB Diagnostic ECG Database. The second database has two classes. The techniques used in these two datasets are the CNN model, CNN + LSTM, and CNN + LSTM + Attention Model. 80% of the data is used for the training, and the remaining 20% is used for testing. The result achieved by using these three techniques shows the accuracy of 99.12% for the CNN model, 99.3% for CNN + LSTM, and 99.29% for CNN + LSTM + Attention Model.

In this paper, we investigate the implementations of newly introduced nonlocal differential operators as convolution of power law, exponential decay law, and the generalized Mittag-Leffler law with fractal derivative in fluid dynamics. The new operators are referred as fractal-fractional differential operators. The governing equations for the problem are constructed with the fractal-fractional differential operators. We present the stability analysis and the error analysis.

<jats:p>A measurement of the molecular topology of graphs is known as a topological index, and several physical and chemical properties such as heat formation, boiling point, vaporization, enthalpy, and entropy are used to characterize them. Graph theory is useful in evaluating the relationship between various topological indices of some graphs derived by applying certain graph operations. Graph operations play an important role in many applications of graph theory because many big graphs can be obtained from small graphs. Here, we discuss two graph operations, i.e., double graph and strong double graph. In this article, we will compute the topological indices such as geometric arithmetic index <jats:inline-formula> <math xmlns="http://www.w3.org/1998/Math/MathML" id="M1"> <mfenced open="(" close=")" separators="|"> <mrow> <mtext>GA</mtext> </mrow> </mfenced> </math> </jats:inline-formula>, atom bond connectivity index <jats:inline-formula> <math xmlns="http://www.w3.org/1998/Math/MathML" id="M2"> <mfenced open="(" close=")" separators="|"> <mrow> <mtext>ABC</mtext> </mrow> </mfenced> </math> </jats:inline-formula>, forgotten index <jats:inline-formula> <math xmlns="http://www.w3.org/1998/Math/MathML" id="M3"> <mfenced open="(" close=")" separators="|"> <mrow> <mi>F</mi> </mrow> </mfenced> </math> </jats:inline-formula>, inverse sum indeg index <jats:inline-formula> <math xmlns="http://www.w3.org/1998/Math/MathML" id="M4"> <mfenced open="(" close=")" separators="|"> <mrow> <mtext>ISI</mtext> </mrow> </mfenced> </math> </jats:inline-formula>, general inverse sum indeg index <jats:inline-formula> <math xmlns="http://www.w3.org/1998/Math/MathML" id="M5"> <msub> <mrow> <mtext>ISI</mtext> </mrow> <mrow> <mfenced open="(" close=")" separators="|"> <mrow> <mi>α</mi> <mo>,</mo> <mi>β</mi> </mrow> </mfenced> </mrow> </msub> </math> </jats:inline-formula>, first multiplicative-Zagreb index <jats:inline-formula> <math xmlns="http://www.w3.org/1998/Math/MathML" id="M6"> <mfenced open="(" close=")" separators="|"> <mrow> <msub> <mrow> <mtext>PM</mtext> </mrow> <mrow> <mn>1</mn> </mrow> </msub> </mrow> </mfenced> <mtext> </mtext> </math> </jats:inline-formula> and second multiplicative-Zagreb index <jats:inline-formula> <math xmlns="http://www.w3.org/1998/Math/MathML" id="M7"> <mfenced open="(" close=")" separators="|"> <mrow> <msub> <mrow> <mtext>PM</mtext> </mrow> <mrow> <mn>2</mn> </mrow> </msub> </mrow> </mfenced> </math> </jats:inline-formula>, fifth geometric arithmetic index <jats:inline-formula> <math xmlns="http://www.w3.org/1998/Math/MathML" id="M8"> <mfenced open="(" close=")" separators="|"> <mrow> <msub> <mrow> <mtext>GA</mtext> </mrow> <mrow> <mn>5</mn> </mrow> </msub> </mrow> </mfenced> </math> </jats:inline-formula>, fourth atom bond connectivity index <jats:inline-formula> <math xmlns="http://www.w3.org/1998/Math/MathML" id="M9"> <mfenced open="(" close=")" separators="|"> <mrow> <msub> <mrow> <mtext>ABC</mtext> </mrow> <mrow> <mn>4</mn> </mrow> </msub> </mrow> </mfenced> </math> </jats:inline-formula> of double graph, and strong double graph of Dutch Windmill graph <jats:inline-formula> <math xmlns="http://www.w3.org/1998/Math/MathML" id="M10"> <msubsup> <mi>D</mi> <mn>3</mn> <mi>p</mi> </msubsup> </math> </jats:inline-formula>.</jats:p>

In this dissertation, a method named Reduction-to-First-Order (RFO) method proposed by L. E. Nicholas Afima [1] in 1991 and first time presented at any forum in 2013 by A. M. Siddiqui and T. Haroon [2] is used to solve the system of third and fourth order boundary value problems. Several examples are presented to get the exact solutions, which illustrate the effectiveness and simplicity of the method.

The starting solutions corresponding to the motions of a Newtonian fluid, between two infinite circular cylinders, are deter- mined by means of the Laplace and finite Hankel transforms. The general case, when both cylinders oscillate along their common axis and around the same axis, is considered. The solutions that have been obtained are presented as sum of the steady-state and transient solutions and satisfy all imposed initial and boundary conditions. Finally, the resulting shear stresses are also determined. The time required to attain the steady-state has been obtained by means of the graphical illustrations.

The electrocardiogram (ECG) is one of the most widely used diagnostic instruments in medicine and healthcare. Deep learning methods have shown promise in healthcare prediction challenges involving ECG data. This paper aims to apply deep learning techniques on the publicly available dataset to classify arrhythmia. We have used two kinds of the dataset in our research paper. One dataset is the MIT-BIH arrhythmia database, with a sampling frequency of 125 Hz with 1,09,446 ECG beats. The classes included in this first dataset are N, S, V, F, and Q. The second database is PTB Diagnostic ECG Database. The second database has two classes. The techniques used in these two datasets are the CNN model, CNN + LSTM, and CNN + LSTM + Attention Model. 80% of the data is used for the training, and the remaining 20% is used for testing. The result achieved by using these three techniques shows the accuracy of 99.12% for the CNN model, 99.3% for CNN + LSTM, and 99.29% for CNN + LSTM + Attention Model.

Pythagorean fuzzy soft set (PFSS) is the most influential and operative extension of the Pythagorean fuzzy set (PFS), which contracts with the parametrized standards of the substitutes. It is also a generalized form of the intuitionistic fuzzy soft set (IFSS) and delivers a well and accurate estimation in the decision-making (DM) procedure. The primary purpose is to prolong and propose ideas related to Einstein’s ordered weighted aggregation operator from fuzzy to PFSS, comforting the condition that the sum of the degrees of membership function and nonmembership function is less than one and the sum of the squares of the degree of membership function and nonmembership function is less than one. We present a novel Pythagorean fuzzy soft Einstein ordered weighted averaging (PFSEOWA) operator based on operational laws for Pythagorean fuzzy soft numbers. Furthermore, some essential properties such as idempotency, boundedness, and homogeneity for the proposed operator have been presented...

The prime objective of the current study is to examine the effects of third-grade hybrid nanofluid with natural convection utilizing the ferro-particle Fe 3 O 4 and titanium dioxide TiO 2 and sodium alginate (SA) as a host fluid, flowing through vertical parallel plates, under the fuzzy atmosphere. The dimensionless highly nonlinear coupled ordinary differential equations are computed adopting the bvp4c numerical approach. This is an extremely effective technique with a low computational cost. For validation, it is found that as the volume fraction of Fe 3 O 4 + TiO 2 hybrid nanoparticles rises, so does the heat transfer rate. The current and existing results with their comparisons are shown in the form of the tables. The present findings are in good agreement with their previous numerical and analytical results in a crisp atmosphere. The nanoparticles volume fraction of Fe 3 O 4 and TiO 2 is taken as uncertain parameters in terms of triangular fuzzy numbers (TFNs) [0, 0.05, 0.1]. T...

The aim of this paper is to propose the generalized version of the multipolar neutrosophic soft set with operations and basic properties. Here, we define the AND, OR, Truth-Favorite, and False-Favorite operators along with their properties. Also, we define the necessity and possibility of operations for them. Later on, to extend it to solve the decision-making problems, we define some information measures such as distance, similarity, and correlation coefficient for the generalized multipolar neutrosophic soft set. Several desirable properties and their relationship between them are derived. Finally, based on these information measures, a decision-making algorithm is stated under the neutrosophic environment to tackle the uncertain and vague information. The applicability of the proposed algorithm is demonstrated through a case study of the medical-diagnosis and the decision-making problems. A comparative analysis with several existing studies reveals the effectiveness of the approach.

Similarity measures (SM) and correlation coefficients (CC) are used to solve many problems. These problems include vague and imprecise information, excluding the inability to deal with general vagueness and numerous information problems. The main purpose of this research is to propose an m-polar interval-valued neutrosophic soft set (mPIVNSS) by merging the m-polar fuzzy set and interval-valued neutrosophic soft set and then study various operations based on the proposed notion, such as AND operator, OR operator, truth-favorite, and false-favorite operators with their properties. This research also puts forward the concept of the necessity and possibility operations of mPIVNSS and also the m-polar interval-valued neutrosophic soft weighted average operator (mPIVNSWA) with its desirable properties. Cosine and set-theoretic similarity measures have been proposed for mPIVNSS using Bhattacharya distance and discussed their fundamental properties. Furthermore, we extend the concept of CC...

For a connected simple graph G , a nonempty subset S of V G is a connected safe set if the induced subgraph G S is connected and the inequality S ≥ D satisfies for each connected component D of G∖S whenever an edge of G exists between S and D . A connected safe set of a connected graph G with minimum cardinality is called the minimum connected safe set and that minimum cardinality is called the connected safe numbers. We study connected safe sets with minimal cardinality of the ladder, sunlet, and wheel graphs.

Topological descriptors are mathematical values related to chemical structures which are associated with different physicochemical properties. The use of topological descriptors has a great contribution in the field of quantitative structure-property relationship (QSPR) and quantitative structure-activity relationship (QSAR) modeling. These are mathematical relationships between different molecular properties or biological activity and some other physicochemical or structural properties. In this article, we calculate few vertex degree-based topological indices/descriptors of the organometallic monolayer structure. At present, the numerical programming of the biological structure with topological descriptors is increasing in consequence in invigorating science, bioinformatics, and pharmaceutics.

The Pythagorean fuzzy hypersoft set (PFHSS) is the most advanced extension of the intuitionistic fuzzy hypersoft set (IFHSS) and a suitable extension of the Pythagorean fuzzy soft set. In it, we discuss the parameterized family that contracts with the multi-subattributes of the parameters. The PFHSS is used to correctly assess insufficiencies, anxiety, and hesitancy in decision-making (DM). It is the most substantial notion for relating fuzzy data in the DM procedure, which can accommodate more uncertainty compared to available techniques considering membership and nonmembership values of each subattribute of given parameters. In this paper, we will present the operational laws for Pythagorean fuzzy hypersoft numbers (PFHSNs) and also some fundamental properties such as idempotency, boundedness, shift-invariance, and homogeneity for Pythagorean fuzzy hypersoft weighted average (PFHSWA) and Pythagorean fuzzy hypersoft weighted geometric (PFHSWG) operators. Furthermore, a novel multic...

The correlation coefficient between two variables plays an important role in statistics. Also, the accuracy of relevance assessment depends on information from a set of discourses. The data collected from numerous statistical studies are full of exceptions. The Pythagorean fuzzy hypersoft set (PFHSS) is a parameterized family that deals with the subattributes of the parameters and an appropriate extension of the Pythagorean fuzzy soft set. It is also the generalization of the intuitionistic fuzzy hypersoft set (IFHSS), which is used to accurately assess insufficiency, anxiety, and uncertainties in decision-making. The PFHSS can accommodate more uncertainties compared to the IFHSS, and it is the most substantial methodology to describe fuzzy information in the decision-making process. The core objective of the this study is to develop the notion and features of the correlation coefficient and the weighted correlation coefficient for PFHSS and to introduce the aggregation operators su...

In this paper, we investigate the multi-criteria decision-making complications under intuitionistic fuzzy hypersoft set (IFHSS) information. The IFHSS is a proper extension of the intuitionistic fuzzy soft set (IFSS) which discusses the parametrization of multi-sub attributes of considered parameters, and accommodates more hesitation comparative to IFSS utilizing the multi sub-attributes of the considered parameters. The main objective of this research is to introduce operational laws for intuitionistic fuzzy hypersoft numbers (IFHSNs). Additionally, based on developed operational laws two aggregation operators (AOs), i.e., intuitionistic fuzzy hypersoft weighted average (IFHSWA) and intuitionistic fuzzy hypersoft weighted geometric (IFHSWG), operators have been presented with their fundamental properties. Furthermore, a decision-making approach has been established utilizing our developed aggregation operators (AOs). Through the established approach, a technique for solving decisio...

The concept of the neutrosophic hypersoft set (NHSS) is a parameterized family that deals with the subattributes of the parameters and is a proper extension of the neutrosophic soft set to accurately assess the deficiencies, anxiety, and uncertainty in decision-making. Compared with existing research, NHSS can accommodate more uncertainty, which is the most significant technique for describing fuzzy information in the decision-making process. The main objective of the follow-up study is to develop the theory of neutrosophic hypersoft matrix (NHSM). The NHSM is the generalized form of a neutrosophic soft matrix (NSM). Some fundamental operations and score function for NHSMs have been introduced with their desirable properties. Furthermore, we introduce the logical operators such as OR-operator and AND-operator with their fundamental properties in the following research. The necessity and possibility operations for NHSMs have been established. Utilizing the developed score function, a...

Correlation coefficients are used to tackle many issues that include indistinct as well as blurred information excluding is not able to deal with the general fuzziness along with obscurity of the problems that have various information. The correlation coefficient (CC) between two variables plays an important role in statistics. Likewise, the accuracy of relevance assessment depends on the information in a set of discourses. The data collected for numerous statistical studies is full of exceptions. The concept of the neutrosophic hypersoft set (NHSS) is a parameterized family that deals with the subattributes of the parameters and is a proper extension of the neutrosophic soft set to accurately assess the deficiencies, anxiety, and uncertainty in decision-making. Compared with existing research, NHSS can accommodate more uncertainty, which is the most significant technique for describing fuzzy information in the decision-making process. The core objective of follow-up research is to ...

In this article, ethylene glycol (EG) + waterbased Maxwell nanofluid with radiation and Soret effects within two parallel plates has been investigated. The problem is formulated in the form of partial differential equations. The dimensionless governing equations for concentration, energy, and momentum are generalized by the fractional molecular diffusion, thermal flux, and shear stress defined by the Caputo–Fabrizio time fractional derivatives. The solutions of the problems are obtained via Laplace inversion numerical algorithm, namely, Stehfest’s. Nanoparticles of silver (Ag) are suspended in a mixture of EG + water to have a nanofluid. It is observed that the thermal conductivity of fluid is enhanced by increasing the values of time and volume fraction. The temperature and velocity of water-silver nanofluid are higher than those of ethylene glycol (EG) + water (H2O)-silver (Ag) nanofluid. The results are discussed at 2% of volume fraction. The results justified the thermo-physical...

Abstract Prime aim of current study is to explore the comparative outcomes for mass and thermal transportation of various fluids models namely Newtonian, micropolar, Williamson and Maxwell due to extending surface. This exploration is concerned to the effect of double diffusion and applied magnetic field. The bioconvection may improve the settling of nanoparticles and the double diffusion effects are considered to be more realistic on the part of this work. The mixture of base fluids with nanoparticles and gyrotactic micro-organisms is homogenous. By the implementation of basic conservation laws, the governing partial differential equations are organized which are then reformed into corresponding ordinary differential equations. For the physical insight, Runga-Kutta method with shooting technique is utilized. The controlling parameters of buoyancy ratio, thermophoresis, magnetic field, Brownian movement, Lewis number and Prandtl number are varied in acceptable ranges to evaluate their impacts on temperature, momentum, concentration field and micro-organisms concentration. The notable outcomes indicated that micropolar fluid takes the highest value for velocity and then Newtonian fluid, Williamson fluid and Maxwell fluid in descending order. The results related to different three non-Newtonian nano-fluids with effective heat transfer can find applications in heat transfer processes such as heat exchanger.

Our aim in this article is to study the radiation and multiple slip effects on magnetohydrodynamic bioconvection flow of micropolar based nanofluid over a stretching surface. In addition, a steering mechanism of making improvements to the Brownian motion and thermophoresis motion of nanoparticles is integrated. The numerical solution of 2-dimensional laminar bioconvective boundary layer flow of micropolar based nanofluids is presented. The basic formulation as partial differential equations is transmuted into ordinary differential equations with the help of suitable similarity transformations. Which are then solved by using the Runge–Kutta method of fourth-order with shooting technique. Some important and relevant characteristics of physical quantities are evaluated via inclusive numerical computations. The influence of vital parameters such as buoyancy parameter λ, bioconvection Rayleigh number Rb, the material parameter K are examined. This investigation showed that with the incre...

It is a theoretical exportation for mass transpiration and thermal transpiration of Casson nanofluid over an extending cylindrical surface. The Stagnation point flow through porous matrix is influenced by magnetic field of form strength. Appropriate similarity functions are availed to yield the transmuted system of leading differential equations. Existence for the solution of momentum equation is proved for various values of Casson parameter β, magnetic parameter M, porosity parameter Kp and Raynolds number Re in two situations of mass transpiration (suction/injuction). Moreover, uniqueness results are discussed and for skin friction factor are established to attain accuracy for large injection values. Thermal and concentration profiles are delineated numerically by applying Runge-Kutta method and shooting technique.

The theory of intuitionistic fuzzy soft set (IFSS) is an extension of the soft set theory which is utilized to precise the deficiency, indeterminacy, and uncertainty of the evaluation while making decisions. The conspicuous characteristic of this mathematical concept is that it considers two distinctive sorts of information, namely the membership and non-membership degrees. The present paper partitioned into two folds: (i) to define the correlation measures for IFSSs; (ii) to introduce the Technique for Order of Preference by Similarity to Ideal Solution(TOPSIS) for IFSS information. Further, few properties identified with these measures are examined thoroughly. In view of these techniques, an approach is presented to solve decision-making problems by utilizing the proposed TOPSIS method based on correlation measures. At last, an illustrative example is enlightened to demonstrate the appropriateness of the proposed approach. Also, its suitability and attainability are checked by contrasting its outcomes and the prevailing methodologies results.

The aim of this report is to study an unsteady mixed convection flow of an incompressible differential type fluid occurrence of chemical reaction that is first order, heat source and radiative heat source with fractional mass diffusion and thermal transports over an infinite vertical plate. The fractional derivative Caputo–Fabrizio which is defined recently with non-singular kernel is used in constitutive laws for the mass and thermal flux, respectively. Semi analytical solutions of the dimensionless concentration, temperature, and velocity fields in addition the rates of heat and mass transfer from the plate to the fluid are established by virtue of the Laplace inversion numerical algorithms Stehfest’s and Tzou’s. Some solutions for ordinary case and obvious results from articles are retrieved as limiting cases. Finally, an impact of flow and fractionalize parameters $$\alpha $$ α and $$\beta $$ β on concentration, temperature and velocity profiles is tabularly and graphically underlined and discussed . We present a valuation between second grade (fractional and ordinary) and viscous (fractional and ordinary) fluids is also interpreted. It is identified that the ordinary fluid has high velocity as comparable to fractional fluids.

Unsteady free convection flows of an incompressible differential type fluid over an infinite vertical plate with fractional thermal transport are studied. Modern definitions of the fractional derivatives in the sense of Atangana–Baleanu (ABC) and Caputo Fabrizio (CF) are used in the constitutive equations for the thermal flux. Exact solutions in both cases of the (ABC) and (CF) derivatives for the dimensionless temperature and velocity fields are established by using the Laplace transform technique. Solutions for the ordinary case and some well-known results from the literature are recovered as a limiting case. Expressions for Nusselt number and Skin friction coefficient are also determined. The influence of the pertinent parameters on temperature and velocity fields are discussed graphically. A comparison of ordinary model, and (ABC) and (CF) models are also depicted. It is found that memory of the physical aspects of the problem is well explained by fractional order (ABC) and (CF) models as compared to ordinary one. Further it is noted that the (ABC) model is the best fit to explain the memory effect of the temperature and velocity fields.

Abstract Laminar unsteady multilayer axial flows of fractional immiscible Maxwell fluids in a circular cylinder are investigated. The flow of fluids is generated by a time-dependent pressure gradient in the axial direction and by the translational motion of a cylinder along his axis. The considered mathematical model is based on the fractional constitutive equation of Maxwell fluids with Caputo time-fractional derivatives. Analytical solutions for the fractional differential equations of the velocity fields with boundary and interfaces conditions have been determined by using the Laplace transform coupled with the Hankel transform of order zero and the Weber transform of order zero. The influence of the memory effects on the motion of the fluid has been investigated for the particular case of three fractional Maxwell fluids. It is found that for increasing values of the fractional parameter the fluid velocity is decreasing. The memory effects have a stronger influence on the velocity of the second layer.

Abstract The unsteady free convection flow, with heat and mass transfer, of an electrically conducting viscoelastic fluid, through a porous medium of variable permeability is investigated. The flow domain is a half space, bounded by a vertical porous plate, with the constant heat flux, constant concentration and a rectilinear translation in its plane with constant velocity. The applied magnetic field of uniform strength is perpendicular to the plate and the magnetic lines of force are fixed relative to plate or, to fluid. Permeability of the porous medium decreases exponentially, with respect to time t, relative to a constant mean value. The closed forms of the temperature, concentration and velocity fields are determined by means of the Laplace transform and method of separation of variables. Numerical calculations are carried out and graphically displayed in order to study the effects of several parameters such as Hartmann number, permeability of porous medium, Prandtl number, heat source/sink parameter, Schmidt number, chemical reaction parameter. The numerical results show that, if the applied magnetic field is fixed to the plate the fluid flows more slowly than if the magnetic field is fixed to fluid. If the magnetic field strength is high, the fluid moves more slowly than into weak magnetic fields.