SOLUTION OF FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS BY HOMOTOPY ANALYSIS METHOD

In this article, the homotopy analysis method (HAM) has been employed to obtain the solution of fractional integro-differential equations of the form D * αy(t) =p(t)y( t) + f (t) + ∫^t/0 k(t,s)F(y(s)) ds , 0 α 1 Where the fractional derivative is described in the Caputo sense. We shall employ here two approaches based on homotopy analysis method first for the linear fractional integro-differential equations and second for the nonlinear fractional integro-differential equations. This indicates the validity and great potential of the homotopy analysis method for solving such types of equations.