New approach to approximate the solution for the system of fractional order Volterra integro-differential equations

Abstract

The main aim of this article is the extension of Optimal Homotopy Asymptotic Method to the system of fractional order integro-differential equations. The systems of fractional order Volterra integro-differential equations (SFIDEs) are taken as test examples. The fractional order derivatives are defined in the Caputo fractional form and the optimal values of auxiliary constants are calculated using the well-known method of least squares. The results obtained by proposed scheme are very encouraging and show close resemblance with exact values. Hence it will be more appealing for the researchers to apply the proposed scheme to different fractional order systems arising in different fields of sciences especially in fluid dynamics and bio-engineering. Keywords: Fractional derivative, OHAM, System of fractional order integro-differential equations, Approximate solution, Caputo derivatives