SOLUTION OF FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS BY HOMOTOPY ANALYSIS METHOD

Abstract

fractional integro-differential equations of the formt*0D y(t) p(t)y(  t)  f (t)   k(t,s)F(y(s)) ds , 0 <  < 1Where the fractional derivative is described in the Caputo sense. We shall employ here twoapproaches based on homotopy analysis method first for the linear fractional integro-differentialequations and second for the nonlinear fractional integro-differential equations. This indicates thevalidity and great potential of the homotopy analysis method for solving such types of equations