Abstract
Our purpose of this paper is to apply the improved Kudryashov method for solving various types of nonlinear fractional partial differential equations. As an application, the time-space fractional Korteweg-de Vries-Burger (KdV-Burger) equation is solved using this method and we get some new travelling wave solutions. To acquire our purpose a complex transformation has been also used to reduce nonlinear fractional partial differential equations to nonlinear ordinary differential equations of integer order, in the sense of the Jumarie’s modified Riemann-Liouville derivative. Afterwards, the improved Kudryashov method is implemented and we get our required reliable solutions where the results are justified by mathematical software Maple-13.
Highlights
IntroductionFractional differential equations have a significant role in describing the complicated nonlinear physical phenomena such as the fluid flow, viscoelasticity, signal processing, control theory, systems identification, biology, physics and other areas [1]-[6]
Fractional differential equations have a significant role in describing the complicated nonlinear physical phenomena such as the fluid flow, viscoelasticity, signal processing, control theory, systems identification, biology, physics and other areas [1]-[6].Fractional differential equations are generalizations of classical differential equations of integer order
Afterwards, the improved Kudryashov method is implemented and we get our required reliable solutions where the results are justified by mathematical software Maple-13
Summary
Fractional differential equations have a significant role in describing the complicated nonlinear physical phenomena such as the fluid flow, viscoelasticity, signal processing, control theory, systems identification, biology, physics and other areas [1]-[6]. The improved Kudryashov method [13] is a similar method to these above methods and the basic principle of this method is to solve nonlinear partial differential equations analytically. This method is straight forward and easy for finding exact solutions FPDEs. In this article, the improved Kudryashov method has been applied to find the new exact travelling wave solutions of the nonlinear time-space fractional order.
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