A COMPARISON OF NUMERICAL METHODS FOR SOLVING FRACTIONAL VOLTERRA INTEGRAL EQUATION OF THE SECOND KIND

Abstract

Fractional Volterra integral equations of the second kind provide an effective mathematical framework for modeling complex phenomena in physics, engineering and biology where traditional integral-order methods prove inadequate.

The main objective of this research is to compare several numerical methods for solving fractional Volterra integral equations of the second kind.

We start by reviewing some of the fundamental concepts of fractional Volterra integral equations and their solvability. Moreover, we address the numerical methods used to solve fractional Volterra integral equations of the second kind, namely, the Haar wavelet collocation method, the Bernstein polynomial collocation method and the spectral Galerkin projection method. Their convergence and stability properties together with their error analysis associated with the proposed numerical methods have been investigated.

These numerical methods are illustrated through some numerical examples. Numerical results show clearly that the Galerkin method provides more efficient and accurate results.