jzs-10859

Numerical Treatments for Nonlinear Integro-Fractional Differential Equations of Volterra-Hammerstein Type using Runge-Kutta Method with the aid of Finite Difference Approximation

Shazad Shawki Ahmed1* &   Mariwan Rashid Ahmed2

1 Sulaimani University, College of Science, Department of Mathematics, Sulaimaniyah-Iraq.

2 Charmo University, College of Medicals and Applied Sciences, Department of Applied Computer, Chamchamal-Iraq    

*Corresponding author E-mail: shazad.ahmed@univsul.edu.iq

DOI Link: https://doi.org/10.17656/jzs.10859

Abstract 

This paper presents a numerical solution scheme for an important class of nonlinear integro-fractional differential equations in Volterra-Hammerstein type of all positive arbitrary orders which are less than or equal to one. In this approach the nonlinear integro-differential equations are expressed in terms of Caputo type fractional derivative. An approach based on the Runge-Kutta methods including second, third and fourth orders with the aid of finite difference approximation. Further, we suggested an algorithm for these methods and for each algorithm the Computer program in MatLab was written in general forms. Finally, several illustrative examples are presented to show the effectiveness and accuracy of this method.

Key Words: Integro-Fractional Differential Equation, Caputo derivative, Finite-difference approximation, Runge-Kutta method

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