Title: Approximate solution of fractional differential equations using Shannon wavelet operational matrix method
Authors: Javid Iqbal; Rustam Abass; Puneet Kumar
Addresses: Department of Mathematical Sciences, BGSB University, Rajouri-185234, J&K, India ' Department of Mathematical Sciences, BGSB University, Rajouri-185234, J&K, India ' Department of Applied Sciences, Dronacharya College, Greater Noida-201308, U.P., India
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.
Keywords: Shannon wavelets; operational matrix method; fractional differential equation; numerical computation; MATLAB.
International Journal of Computing Science and Mathematics, 2021 Vol.13 No.3, pp.228 - 244
Received: 26 Jan 2018
Accepted: 10 Apr 2018
Published online: 02 Aug 2021 *