Gegenbauer Wavelet Solutions of Fractional Integro-Differential Equations

Abstract

The aim of this study is to use Gegenbauer wavelets in the solution of fractional integrodifferential equations. The method is applied to several problems with different values of resolution parameter and the degree of the truncated polynomial. The results are compared with those obtained from other numerical methods. We observe that the current method is very effective and gives accurate results. One of the reasons for that is it enables us to improve accuracy by increasing resolution parameter, while keeping the degree of polynomial fixed. Another reason is nonlinear terms do not require linearization. Hence the method can be directly implemented and results in the system of algebraic equations which solved by Wolfram Mathematica. It can be asserted that this is the first application of the Gegenbauer wavelet method to the aforementioned types of problems. (C) 2022 Elsevier B.V. All rights reserved.