Numerical Solution of Fractional-Order Fredholm Integrodifferential Equation in the Sense of Atangana–Baleanu Derivative

Author:

Wang Jian1,Kamran 2ORCID,Jamal Ayesha2,Li Xuemei3ORCID

Affiliation:

1. Department of Basic Education and Research, Changchun Sci-Tech University, Changchun 130000, China

2. Department of Mathematics, Islamia College Peshawar, Khyber Pakhtoon Khwa, Peshawar, Pakistan

3. School of Architecture and Civil Engineering, Changchun Sci-Tech University, Changchun 130000, China

Abstract

In the present article, our aim is to approximate the solution of Fredholm-type integrodifferential equation with Atangana–Baleanu fractional derivative in Caputo sense. For this, we propose a method based on Laplace transform and inverse LT. In our numerical scheme, the given equation is transformed to an algebraic equation by employing the Laplace transform. The reduced equation will be solved in complex plane. Finally, the solution of the given problem is obtained via inverse Laplace transform by representing it as a contour integral. Then, the trapezoidal rule is used to approximate the integral to high accuracy. We have considered linear and nonlinear fractional Fredholm integrodifferential equations to validate our method.

Publisher

Hindawi Limited

Subject

General Engineering,General Mathematics

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