Approximate solution of fractional differential equations using Shannon wavelet operational matrix method

Abstract

Many physical problems are frequently governed by fractional differential equations and obtaining the solution of these equations have been the subject of a lot of investigations in recent years. The aim of this paper is to propose a novel and effective method based on Shannon wavelet operational matrices of fractional-order integration. The theory of Shannon wavelets and its properties are first presented. Block Pulse functions and collocation method are employed to derive a general procedure in constructing these operational matrices. The main peculiarity of the proposed technique is that it condenses the given problem into a system of algebraic equations that can be easily solved by MATLAB package. Furthermore, a designed scheme is applied to numerical examples to analyse its applicability, reliability, and effectiveness.