The aim of this paper is to find the exact solution of linear fuzzy fractional differential equat... more The aim of this paper is to find the exact solution of linear fuzzy fractional differential equation. Shehu Transform method has been introduced to solve the fuzzy fractional initial value problems. Fractional derivatives are considered in Caputo sense. This method is a powerful tool to find the solution of fuzzy fractional differential equations. Numerical examples show the efficiency of the proposed method.
Objectives: In applied sciences and engineering, fuzzy fractional differential equations (FFDEs) ... more Objectives: In applied sciences and engineering, fuzzy fractional differential equations (FFDEs) and fuzzy fractional integral equations (FFIEs) are a crucial topic. The main objective of this work is to discover an analytical approximate solution for the fuzzy fractional Volterra-Fredholm integro differential equations (FFVFIDE). In the Caputo concept, fractional derivatives are regarded. Methods: The Shehu transform is challenging to exist for nonlinear problems. So, the Shehu transform is combined with the Adomian decomposition method is called the Shehu Adomian decomposition method (SHADM) and has been proposed to solve both linear and nonlinear FFVFIDEs. Findings: Both linear and nonlinear FFVIFIDEs can be solved using this technique. For nonlinear terms, Adomian polynomials have been used. The main benefit of this approach is that it converges quickly to the exact solution. Figures and numerical examples demonstrate the expertise of the suggested approach. Novelty: The comparison between the exact solution and numerical solution is shown in figures for various values of fractional order α. The numerical evolution demonstrates the efficiency and reliability of the proposed SHADM. The proposed approach is rapid, exact, and simple to apply and produce excellent outcomes.
Objectives: In applied sciences and engineering, fuzzy fractional differential equations (FFDEs) ... more Objectives: In applied sciences and engineering, fuzzy fractional differential equations (FFDEs) and fuzzy fractional integral equations (FFIEs) are a crucial topic. The main objective of this work is to discover an analytical approximate solution for the fuzzy fractional Volterra-Fredholm integro differential equations (FFVFIDE). In the Caputo concept, fractional derivatives are regarded. Methods: The Shehu transform is challenging to exist for nonlinear problems. So, the Shehu transform is combined with the Adomian decomposition method is called the Shehu Adomian decomposition method (SHADM) and has been proposed to solve both linear and nonlinear FFVFIDEs. Findings: Both linear and nonlinear FFVIFIDEs can be solved using this technique. For nonlinear terms, Adomian polynomials have been used. The main benefit of this approach is that it converges quickly to the exact solution. Figures and numerical examples demonstrate the expertise of the suggested approach. Novelty: The comparison between the exact solution and numerical solution is shown in figures for various values of fractional order α. The numerical evolution demonstrates the efficiency and reliability of the proposed SHADM. The proposed approach is rapid, exact, and simple to apply and produce excellent outcomes.
Objectives: In applied sciences and engineering, fuzzy fractional differential equations (FFDEs) ... more Objectives: In applied sciences and engineering, fuzzy fractional differential equations (FFDEs) are a crucial topic. The main objective of this study is to find the exact solution of the nonlinear Fuzzy Fractional Biological Population Model (FFBPM). In the Caputo concept, fractional derivatives are regarded. Methods: For nonlinear problems, the Shehu transform is difficult to exist. So, the Shehu transform is combined with the Adomian decomposition method is called the Shehu Adomian Decomposition Method (SHADM) and has been proposed to solve the FFBPM. Findings: The main favor of this method is rapidly converging to the exact solution for nonlinear FFDEs. The theoretical proof of convergence for the SHADM and the uniqueness of the solution is given. Novelty: Adomian polynomials are used for nonlinear terms. Figures and numerical examples demonstrate the expertise of the suggested approach. This method is applied for both linear and nonlinear ordinary and partial FFDEs. The proposed approach is rapid, exact, and simple to apply and produce excellent outcomes.
The objective of this research is to determine the approximate solution to Fuzzy Fractional Diffe... more The objective of this research is to determine the approximate solution to Fuzzy Fractional Differential Equations (FFDEs). For Fuzzy Fractional Initial Value Problems (FFIVPs), the methods called Fuzzy Fractional Fourth Order Runge-Kutta method based on Root Mean Square (FFRK4RM) and called Fuzzy Fractional Fourth Order Runge-Kutta method based on Contraharmonic Mean (FFRK4CoM) is developed. In this paper, both linear and nonlinear FFDEs can be solved using triangular and trapezoidal fuzzy numbers. FFRRK4RM and FFRK4CoM can be compared. The tables gives the absolute error between the exact and approximate solutions. From the graphical results, the approximate solution approaches the exact result very closely as the step size gets smaller. The outcomes show that the suggested approach is easy to use, accurate, clear, and convenient for solving both linear and nonlinear FFIVP.
The aim of this paper is to find the exact solution of linear fuzzy fractional differential equat... more The aim of this paper is to find the exact solution of linear fuzzy fractional differential equation. Shehu Transform method has been introduced to solve the fuzzy fractional initial value problems. Fractional derivatives are considered in Caputo sense. This method is a powerful tool to find the solution of fuzzy fractional differential equations. Numerical examples show the efficiency of the proposed method.
Objectives: In applied sciences and engineering, fuzzy fractional differential equations (FFDEs) ... more Objectives: In applied sciences and engineering, fuzzy fractional differential equations (FFDEs) and fuzzy fractional integral equations (FFIEs) are a crucial topic. The main objective of this work is to discover an analytical approximate solution for the fuzzy fractional Volterra-Fredholm integro differential equations (FFVFIDE). In the Caputo concept, fractional derivatives are regarded. Methods: The Shehu transform is challenging to exist for nonlinear problems. So, the Shehu transform is combined with the Adomian decomposition method is called the Shehu Adomian decomposition method (SHADM) and has been proposed to solve both linear and nonlinear FFVFIDEs. Findings: Both linear and nonlinear FFVIFIDEs can be solved using this technique. For nonlinear terms, Adomian polynomials have been used. The main benefit of this approach is that it converges quickly to the exact solution. Figures and numerical examples demonstrate the expertise of the suggested approach. Novelty: The comparison between the exact solution and numerical solution is shown in figures for various values of fractional order α. The numerical evolution demonstrates the efficiency and reliability of the proposed SHADM. The proposed approach is rapid, exact, and simple to apply and produce excellent outcomes.
Objectives: In applied sciences and engineering, fuzzy fractional differential equations (FFDEs) ... more Objectives: In applied sciences and engineering, fuzzy fractional differential equations (FFDEs) and fuzzy fractional integral equations (FFIEs) are a crucial topic. The main objective of this work is to discover an analytical approximate solution for the fuzzy fractional Volterra-Fredholm integro differential equations (FFVFIDE). In the Caputo concept, fractional derivatives are regarded. Methods: The Shehu transform is challenging to exist for nonlinear problems. So, the Shehu transform is combined with the Adomian decomposition method is called the Shehu Adomian decomposition method (SHADM) and has been proposed to solve both linear and nonlinear FFVFIDEs. Findings: Both linear and nonlinear FFVIFIDEs can be solved using this technique. For nonlinear terms, Adomian polynomials have been used. The main benefit of this approach is that it converges quickly to the exact solution. Figures and numerical examples demonstrate the expertise of the suggested approach. Novelty: The comparison between the exact solution and numerical solution is shown in figures for various values of fractional order α. The numerical evolution demonstrates the efficiency and reliability of the proposed SHADM. The proposed approach is rapid, exact, and simple to apply and produce excellent outcomes.
Objectives: In applied sciences and engineering, fuzzy fractional differential equations (FFDEs) ... more Objectives: In applied sciences and engineering, fuzzy fractional differential equations (FFDEs) are a crucial topic. The main objective of this study is to find the exact solution of the nonlinear Fuzzy Fractional Biological Population Model (FFBPM). In the Caputo concept, fractional derivatives are regarded. Methods: For nonlinear problems, the Shehu transform is difficult to exist. So, the Shehu transform is combined with the Adomian decomposition method is called the Shehu Adomian Decomposition Method (SHADM) and has been proposed to solve the FFBPM. Findings: The main favor of this method is rapidly converging to the exact solution for nonlinear FFDEs. The theoretical proof of convergence for the SHADM and the uniqueness of the solution is given. Novelty: Adomian polynomials are used for nonlinear terms. Figures and numerical examples demonstrate the expertise of the suggested approach. This method is applied for both linear and nonlinear ordinary and partial FFDEs. The proposed approach is rapid, exact, and simple to apply and produce excellent outcomes.
The objective of this research is to determine the approximate solution to Fuzzy Fractional Diffe... more The objective of this research is to determine the approximate solution to Fuzzy Fractional Differential Equations (FFDEs). For Fuzzy Fractional Initial Value Problems (FFIVPs), the methods called Fuzzy Fractional Fourth Order Runge-Kutta method based on Root Mean Square (FFRK4RM) and called Fuzzy Fractional Fourth Order Runge-Kutta method based on Contraharmonic Mean (FFRK4CoM) is developed. In this paper, both linear and nonlinear FFDEs can be solved using triangular and trapezoidal fuzzy numbers. FFRRK4RM and FFRK4CoM can be compared. The tables gives the absolute error between the exact and approximate solutions. From the graphical results, the approximate solution approaches the exact result very closely as the step size gets smaller. The outcomes show that the suggested approach is easy to use, accurate, clear, and convenient for solving both linear and nonlinear FFIVP.
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