Dr. Zeyad Al-Zhour
Head of Department of Basic Sciences and Humanities,
College of Engineering,
University of Dammam,
Dammam,
Saudi Arabia ,
Emails: zalzhour@ud.edu.sa ; zeyad1968@yahoo.com Supervisors: Prof. Dr. Adem Kilicman
Abstract In this paper, we present numerical analytical solutions of a fractional multi-pantograp... more Abstract In this paper, we present numerical analytical solutions of a fractional multi-pantograph system by using two attractive methods with rapidly convergence, control of the convergence region and easily software accounts of the infinite series solutions. These methods are: The homotopy analysis and residual power series methods. Furthermore, two important and interesting problems related to the linear nonhomogeneous fractional pantograph system are formulated from the fractional multi-pantograph system and solved numerically and graphically by using the above-mentioned methods. Finally, we show that the approximate and exact solutions are coinciding with a slight difference in error.
The neutron diffusion equation (NDE) is one of the most important partial differential equations ... more The neutron diffusion equation (NDE) is one of the most important partial differential equations (PDEs), to describe the neutron behavior in nuclear reactors and many physical phenomena. In this paper, we reformulate this problem via Caputo fractional derivative with integer-order initial conditions, whose physical meanings, in this case, are very evident by describing the whole-time domain of physical processing. The main aim of this work is to present the analytical exact solutions to the fractional neutron diffusion equation (F-NDE) with one delayed neutrons group using the Laplace transform (LT) in the sense of the Caputo operator. Moreover, the poles and residues of this problem are discussed and determined. To show the accuracy, efficiency, and applicability of our proposed technique, some numerical comparisons and graphical results for neutron flux simulations are given and tested at different values of time $ t $ and order $ \alpha $ which includes the exact solutions (when ...
In this paper, we present the series solutions of the nonlinear time-fractional coupled Boussines... more In this paper, we present the series solutions of the nonlinear time-fractional coupled Boussinesq-Burger equations (T-FCB-BEs) using Laplace-residual power series (L-RPS) technique in the sense of Caputo fractional derivative (C-FD). To assert the efficiency, simplicity, performance, and reliability of our proposed method, an attractive and interesting numerical example is tested analytically and graphically. In addition, our obtained results show that this algorithm is compatible and accurate for investigating the fractional-order solutions of engineering and physical applications. Finally, Mathematica software 14 is applied to compute the numerical and graphical results.
This paper is concerned with two generalizations of Ando’s geometric mean and two related general... more This paper is concerned with two generalizations of Ando’s geometric mean and two related generalizations of the Tracy-Singh product for partitioned matrices. We recover the relationship between the Ando’s geometric mean and the Kronecker product to the case of operator mean and Tracy-Singh product. We provide several operator inequalities associated with non-negative linear maps by means of concavity and convexity theorems. We apply the concavity and convexity theorems in order to obtain new unusual estimates for the Khatri-Rao product positive definite matrices. Finally, the results lead inequalities involving Hadamard product and Ando’s (α − power) geometric mean, as a special case.
Abstract: In this paper, we formulate the linear singular and non-singular fractional time-varyin... more Abstract: In this paper, we formulate the linear singular and non-singular fractional time-varying descriptor system and present the general exact solutions of both cases in Caputo sense. Furthermore, two illustrated examples are also given to show our new approach. Keywords: Time-Varying Descriptor System; Kronecker Product; Mittag-Leffler Matrix. AMS 2000 Mathematics Subject Classification: 15A24; 15A30
... Mohd. Salmi Md.Noorani Universiti Kebangsaan Malaysia, Malaysia. Monica Nevins University of ... more ... Mohd. Salmi Md.Noorani Universiti Kebangsaan Malaysia, Malaysia. Monica Nevins University of Ottawa, Canada ... Said Kouachi Qassim University, Saudi Arabia Samir Kumar Bhowmik University of Amsterdam, Netherlands Santosh Kumar Victoria University, Australia ...
In this paper, a family of geometric means for positive matrices is studied; provided some counte... more In this paper, a family of geometric means for positive matrices is studied; provided some counter examples are given. It stills an open problem to find a completely satisfactory definition. We generalize the geometric means of two positive matrices to arrive the definitions of the weighted means of k positive matrices. Some new connections between the Tracy-Singh product and geometric means of positive matrices are established. The results lead to the case of Kronecker product of positive matrices.
Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering, 2021
The two-dimensional magnetohydrodynamics incompressible flow of nanofluid about a stretching surf... more The two-dimensional magnetohydrodynamics incompressible flow of nanofluid about a stretching surface is investigated with the existence of viscous dissipation and Joule heating. Moreover, the impact of the convective condition and mass suction is applied with the viscous nanofluid containing copper nanoparticles and the base fluid water. The similarity variables have been employed to transform the coupled nonlinear partial differential equations into the ordinary differential equations and the numerical scheme bp4c is implemented for the further analysis of the solution. The diverse results of temperature, skin friction coefficient, velocity, and the Nusselt number according to numerous parameters have been shown graphically. It appears that the Nusselt number and the skin friction reduces, which is caused by the enhancement of both Hartman number and nanoparticles concentration. Moreover, the fluid temperature surges with the growth of Biot number, and Eckert number whereas the gro...
Abstract In this paper, we present numerical analytical solutions of a fractional multi-pantograp... more Abstract In this paper, we present numerical analytical solutions of a fractional multi-pantograph system by using two attractive methods with rapidly convergence, control of the convergence region and easily software accounts of the infinite series solutions. These methods are: The homotopy analysis and residual power series methods. Furthermore, two important and interesting problems related to the linear nonhomogeneous fractional pantograph system are formulated from the fractional multi-pantograph system and solved numerically and graphically by using the above-mentioned methods. Finally, we show that the approximate and exact solutions are coinciding with a slight difference in error.
The neutron diffusion equation (NDE) is one of the most important partial differential equations ... more The neutron diffusion equation (NDE) is one of the most important partial differential equations (PDEs), to describe the neutron behavior in nuclear reactors and many physical phenomena. In this paper, we reformulate this problem via Caputo fractional derivative with integer-order initial conditions, whose physical meanings, in this case, are very evident by describing the whole-time domain of physical processing. The main aim of this work is to present the analytical exact solutions to the fractional neutron diffusion equation (F-NDE) with one delayed neutrons group using the Laplace transform (LT) in the sense of the Caputo operator. Moreover, the poles and residues of this problem are discussed and determined. To show the accuracy, efficiency, and applicability of our proposed technique, some numerical comparisons and graphical results for neutron flux simulations are given and tested at different values of time $ t $ and order $ \alpha $ which includes the exact solutions (when ...
In this paper, we present the series solutions of the nonlinear time-fractional coupled Boussines... more In this paper, we present the series solutions of the nonlinear time-fractional coupled Boussinesq-Burger equations (T-FCB-BEs) using Laplace-residual power series (L-RPS) technique in the sense of Caputo fractional derivative (C-FD). To assert the efficiency, simplicity, performance, and reliability of our proposed method, an attractive and interesting numerical example is tested analytically and graphically. In addition, our obtained results show that this algorithm is compatible and accurate for investigating the fractional-order solutions of engineering and physical applications. Finally, Mathematica software 14 is applied to compute the numerical and graphical results.
This paper is concerned with two generalizations of Ando’s geometric mean and two related general... more This paper is concerned with two generalizations of Ando’s geometric mean and two related generalizations of the Tracy-Singh product for partitioned matrices. We recover the relationship between the Ando’s geometric mean and the Kronecker product to the case of operator mean and Tracy-Singh product. We provide several operator inequalities associated with non-negative linear maps by means of concavity and convexity theorems. We apply the concavity and convexity theorems in order to obtain new unusual estimates for the Khatri-Rao product positive definite matrices. Finally, the results lead inequalities involving Hadamard product and Ando’s (α − power) geometric mean, as a special case.
Abstract: In this paper, we formulate the linear singular and non-singular fractional time-varyin... more Abstract: In this paper, we formulate the linear singular and non-singular fractional time-varying descriptor system and present the general exact solutions of both cases in Caputo sense. Furthermore, two illustrated examples are also given to show our new approach. Keywords: Time-Varying Descriptor System; Kronecker Product; Mittag-Leffler Matrix. AMS 2000 Mathematics Subject Classification: 15A24; 15A30
... Mohd. Salmi Md.Noorani Universiti Kebangsaan Malaysia, Malaysia. Monica Nevins University of ... more ... Mohd. Salmi Md.Noorani Universiti Kebangsaan Malaysia, Malaysia. Monica Nevins University of Ottawa, Canada ... Said Kouachi Qassim University, Saudi Arabia Samir Kumar Bhowmik University of Amsterdam, Netherlands Santosh Kumar Victoria University, Australia ...
In this paper, a family of geometric means for positive matrices is studied; provided some counte... more In this paper, a family of geometric means for positive matrices is studied; provided some counter examples are given. It stills an open problem to find a completely satisfactory definition. We generalize the geometric means of two positive matrices to arrive the definitions of the weighted means of k positive matrices. Some new connections between the Tracy-Singh product and geometric means of positive matrices are established. The results lead to the case of Kronecker product of positive matrices.
Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering, 2021
The two-dimensional magnetohydrodynamics incompressible flow of nanofluid about a stretching surf... more The two-dimensional magnetohydrodynamics incompressible flow of nanofluid about a stretching surface is investigated with the existence of viscous dissipation and Joule heating. Moreover, the impact of the convective condition and mass suction is applied with the viscous nanofluid containing copper nanoparticles and the base fluid water. The similarity variables have been employed to transform the coupled nonlinear partial differential equations into the ordinary differential equations and the numerical scheme bp4c is implemented for the further analysis of the solution. The diverse results of temperature, skin friction coefficient, velocity, and the Nusselt number according to numerous parameters have been shown graphically. It appears that the Nusselt number and the skin friction reduces, which is caused by the enhancement of both Hartman number and nanoparticles concentration. Moreover, the fluid temperature surges with the growth of Biot number, and Eckert number whereas the gro...
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