New Solitary Wave Solutions of Generalized Space-Time Fractional Fifth Order Laxs and Sawada Kotera KdV Type Equations in Mathematical Physics

摘要

In the modern advancement, space-time fractional-order problems are very essential in many fields of physics and applied mathematics, it always needed to devise the techniques for solutions of such equations. This paper is devoted to proposed the new fast hybrid methods based on reduced differential transform method (RDTM) and variational iteration method (VIM) with the fractional complex transform (FCT) to solve the generalized space-time fractional fifth order Korteweg-de Vries (KdV) equations to get the solitary wave solutions. In this paper, fractional fifth order Lax's KdV and Sawada Kotera equations are discussed with modified Riemann-Liouville fractional derivative which have never been studied before. The comparison of highly approximated solutions show that the FCT with the help of RDTM is more accurate than VIM with FCT. This is seen when the solutions are compared with the exact solutions at α= β =1, and also shows the perfectness, accuracy, simplicity and less computational cost of this new hybrid computational approach. Numerical results are obtained for verification and demonstration purpose by using Mathematica software.