Numerical Treatment of Volterra-Fredholm Integro- Differential Equations of Fractional Order and its Convergence Analysis

Abstract

This work deals with semi-analytical and numerical methods to solve a class of fractional order Volterra-Fredholm integro-differential equations. First, a semi-analytical method is proposed using the Chebyshev and Bernstein polynomials in the Adomian decomposition method. The uniqueness of the solution and convergence of the method are proved. Further, we solve the model using a numerical scheme comparing the L1 scheme for the fractional order derivative in combination with appropriate quadrature rules for the integral parts. Numerical experiments are done by the proposed methods to show their efficiency through a few tabular data and plots. Some comparisons with the existing results show that the proposed methods are highly productive and reliable.