An Effective Numerical Scheme for Fractional Integro-Differential Equation Systems Using Hermite Wavelets

Numerous mathematical models, such as elasticity, nuclear reactor dynamics, and heat conduction in memory materials, use systems of fractional integro-differential equations, or FIDEs. In this research, the numerical solution of linear and nonlinear systems of FIDEs is obtained by means of an operational matrix approach based on Hermite wavelets. Using the operational matrix of the Hermite wavelets, the FIDE is transformed into an algebraic equation, and the solution of that algebraic equation is obtained. Three numerical examples are provided to show the accuracy and consistency of the suggested technique.