On the Wavelet Collocation Method for Solving Fractional Fredholm Integro-Differential Equations

Haifa Bin Jebreen and Ioannis Dassios
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Haifa Bin Jebreen: Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
Ioannis Dassios: AMPSAS, University College Dublin, D04 V1W8 Dublin, Ireland

Mathematics, 2022, vol. 10, issue 8, 1-12

Abstract: An efficient algorithm is proposed to find an approximate solution via the wavelet collocation method for the fractional Fredholm integro-differential equations (FFIDEs). To do this, we reduce the desired equation to an equivalent linear or nonlinear weakly singular Volterra–Fredholm integral equation. In order to solve this integral equation, after a brief introduction of Müntz–Legendre wavelets, and representing the fractional integral operator as a matrix, we apply the wavelet collocation method to obtain a system of nonlinear or linear algebraic equations. An a posteriori error estimate for the method is investigated. The numerical results confirm our theoretical analysis, and comparing the method with existing ones demonstrates its ability and accuracy.

Keywords: wavelet collocation method; fractional integro-differential equation; Müntz–Legendre wavelets (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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