Nonlinear shallow water waves: A fractional order approach

Abstract

Nonlinear partial differential equations governing the obscure phenomena of shallow water waves are discussed in this article. Time fractional model is considered to understand the upcoming solutions on the basis of all historical states of the solution. A semi-analytic technique, Homotopy Perturbation Transform Method (HPTM) is used in conjunction with a numerical technique to validate the approximate solutions. With the aid of graphical interpretation, the favorable wave parameters, to avoid wave breaking are estimated.

Keywords

• Fractional calculus
• Fractional KdV equations
• Homotopy method
• Perturbation analysis