Approximate solution of fractional differential equations using Shannon wavelet operational matrix method. (25th July 2021)

• Record Type: Journal Article
• Authors: Iqbal, Javid; Abass, Rustam; Kumar, Puneet
• Is Part Of: International journal of computing science and mathematics. Volume 13:Number 3(2021)
• Page Start: 228
• Page End: 244
• Publication Date: 2021-07-25
• Subjects: Shannon wavelets -- operational matrix method -- fractional differential equation -- numerical computation -- MATLAB; Mathematics -- Periodicals; Computer science -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.285
• Languages: English
• ISSNs: 1752-5055

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.