Numerical method for fractional dispersive partial differential equations

Abstract

In this work, fractional variational iteration method (FVIM) has been applied successfully to find the solution of fractional dispersive partial differential equations of third-order in multi-dimensional spaces. The contemplated graphs explain the character of the solution for different values of fractional order . The mightiness and accurateness of the proposed techniques are studied with the help of two test examples.

Analytical Investigation of Third-Order Time-Fractional Dispersive Partial Differential Equations Using Sumudu Transform Iterative Method

“…The same result was obtained by Pandey and Mishra [16] using HASTM, Prakash and Kumar [18] using FVIM, Ravi Kanth and Aruna [19] using the FDTM and MFDTM.…”

Application of Laplace–Adomian Decomposition Method for the Analytical Solution of Third-Order Dispersive Fractional Partial Differential Equations

“…The solution to non-linear coupled space-time fractional modified KdV equations was obtained by Feng’s first integral method [ 16 ]. Fractional PDEs of order three have been solved by different methods, such as fractional variational iteration method (FVIM) [ 17 ], classical Riccati equations method [ 18 ], fractional differential transform method(FDTM) and modified fractional differential transform method (MFDTM) [ 19 ], spline method (SM) [ 20 ] and homotopy analysis Sumudu transform method (HASTM) [ 21 ].…”

Non-polynomial quintic spline for numerical solution of fourth-order time fractional partial differential equations

“…Pandey and Mishra [11] applied Sumudu transforms and homotopy analysis approach for solving time fractional third-order dispersive type of PDEs. The fractional variational iteration method was put into action by Prakash and Kumar in [12] for series solution to third-order fractional dispersive PDEs in a higher dimensional space.…”