HOMOTOPY ANALYSIS METHOD BASED ON OPTIMAL VALUE OF THE CONVERGENCE CONTROL PARAMETER FOR SOLVING SEMI-DIFFERENTIAL EQUATIONS

In this paper, homotopy analysis method is directly ex- tended to investigate nth order semi-dierential equations and to de- rive their numerical solutions which is introduced by replacing some integer-order space derivatives by fractional derivatives. The fractional derivatives are described in the Caputo sense. So the homotopy analysis method for dierential equations of integer-order is directly extended to derive explicit and numerical solutions of the fractional dierential equa- tions. An optimal value of the convergence control parameter is given through the square residual error. Comparison is made between Homo- topy perturbation method, collocation spline method, and the present method.

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