An efficient computational technique for time-fractional modified Degasperis-Procesi equation arising in propagation of nonlinear dispersive waves

Abstract

In this paper, an efficient hybrid numerical scheme which is based on a joint venture of the q-homotopy analysis method and Sumudu transform is applied to investigate the time-fractional modified Degasperis-Procesi (DP) equation. The present study considers the Caputo fractional derivative. The fractional order modified DP model is very important and plays a great role in study of ocean engineering and science. The proposed scheme provides a beautiful opportunity for proper selection of the auxiliary parameter ℏ and the asymptotic parameter ρ ( ≥ 1) to handle mainly the differential equations of nonlinear nature. The offered scheme produces the solution in the shape of a convergent series in a large admissible domain which is helpful to regulate the region of convergence of a series solution. The proposed work computes the approximate analytical solution of the fractional modified DP equation systematically and also presents graphically the variation of the obtained solution for diverse values of the fractional parameter β.

Keywords

• Fractional Degasperis-Procesi equation
• Nonlinear dispersive waves
• Analytical solution
• q-homotopy analysis method
• Sumudu transform