Haar wavelets method for solving class of coupled systems of linear fractional Fredholm integro-differential equations

Abstract

In this paper, firstly, the “ Haar wavelet method ” is used to give approximate solutions for coupled systems of linear fractional Fredholm integro-differential equations. Moreover, we consider the fractional derivative to be described in the Caputo sense. The general idea of this technique is simply based on reducing this kinds of coupled systems into systems of algebraic equations which are easily to deal with and solve. Also, Laplace transform operator is included to develop a sophisticated approach which we called “ Laplace Haar wavelet method ” as an adjustment to “ Haar wavelet method ” to reduce the error and computational time. We provide illustrative examples to confirm validity, efficiency, accuracy, and applicability of the proposed methods.

Keywords

• Haar wavelet method
• Laplace Haar wavelet method
• Caputo fractional derivative
• Coupled systems of linear fractional Fredhom integro-differential equations
• Numerical solutions