Numerical solution of fractional-order fredholm integrodifferential equation in the sense of atangana-baleanu derivative

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. +e 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.