Numerical Solution of Fractional Order Partial Differential Equation with Sturm-Liouville Problem Using Homotopy Analysis and Homotopy Perturbation Methods

Abstract

This research work is concerned with the application of both homotopy analysis and homotopy perturbation methods to linear and nonlinear, homogeneous, and nonhomogeneous fractional order partial differential equations and fractional order SturmLiouville equation. The fractional order derivatives are interpreted in Caputo sense. The applications of the two semi analytical methods are extended to one dimensional fractional order wave equation. Although homotopy perturbation method involves asymptotic expansion of terms with small parameter, but it pays off in the accuracy of the results obtained through which are similar to results using homotopy analysis method. All the problems selected from the existing literature made provision for results with integral order values, but in the present work we equally present results for fractional order. Our results are presented in 3D graphs and compared well with the existing results in the literature.