Abstract
•We consider a fractional model of dispersive partial differential equation.•Fractional dispersive partial differential equation occurs in water waves.•The HPSTM and ADM are used to examine the fractional problems.•The obtained results are shown graphically and in tabular form.•The results obtained by proposed methods are in an excellent agreement.
This article is devoted to a newly introduced numerical method for time-fractional dispersive partial differential equation in a multi-dimensional space. The time-fractional dispersive partial differential equation plays a great role in solving the problems arising in ocean science and engineering. The numerical technique comprises of Sumudu transform, homotopy perturbation scheme and He's polynomial, namely homotopy perturbation Sumudu transform method (HPSTM) is efficiently used to examine time-fractional dispersive partial differential equation of third order in multi-dimensional space. The approximate analytic solution of the time-fractional dispersive partial differential equation of third-order in multi-dimensional space obtained by HPSTM is compared with exact solution as well as the solution obtained by using Adomain decomposition method. The results derived with the aid of two techniques are in a good agreement and consequently these techniques may be considered as an alternative and efficient approach for solving fractional partial differential equations. Several test problems are experimented to confirm the accuracy and efficiency of the proposed methods.