Numerical Solution of linear Fractional Integro-Differential Equations

Abstract

In this thesis, we tackled the challenging task of numerically solving linear fractional integro-differential equations (FI-DEs), with a particular focus on those involving the Caputo fractional derivative. This class of equations serves as a vital modeling tool for systems exhibiting memory effects and non-local properties, which often lie beyond the scope of classical integer-order models. Given the inherent complexity in finding analytical solutions for these equations, developing efficient numerical methods becomes essential. This thesis successfully presented and applied the spectral collocation method as a robust and effective approach to solve these equations. We began by establishing a solid theoretical foundation.