Numerical Scheme for Solution of Coupled System of Initial Value Fractional Order Fredholm Integro Differential Equations with Smooth Solutions

Abstract

We study shifted  Legendre polynomials and develop some operationalmatrices of integrations. We use these operational matrices anddevelop new sophisticated technique for numerical solutions to acoupled system of fredholm integro differential equations withinitial conditions. We develop  simple procedure to reduce the coupled system to a system of easily solvable algebraicequations without discretizing the system. We provide examples andnumerical simulations to show the applicability and simplicity ofour results and to demonstrate that the results obtained using thenew technique matches well with the exact solutions of the problem.We also provide error analysis