A novel iterative method to solve nonlinear wave-like equations of fractional order with variable coefficients

Abstract

In this work, we suggest a novel iterative method to give approximate solutions of nonlinear wave-like equations of fractional order with variable coefficients. The advantage of the proposed method is the ability to combine two different methods: Shehu transform method and homotopy analysis method, in addition to providing an approximate solution in the form of a convergent series with easily computable components, requiring no linearization or small perturbation. This method can be called Shehu homotopy analysis method (SHAM). Three different examples are presented to illustrate the preciseness and effectiveness of the proposed method. The numerical results show that the solutions obtained by SHAM are in good agreement with the solutions found in the literature. Furthermore, the results show that this method can be implemented in an easy way and therefore can be used to solve other nonlinear fractional partial differential equations.

A New Method for Solving Sequential Fractional Wave Equations

“…In [18,19], the collocation method and series method are employed to solve fractional initial value problems (IVPs), respectively. However, [20] presents an iterative method developed for solving such problems. Te operational matrix method is used to solve systems of fractional IVPs in [21].…”