Application of the Improved Kudryashov Method to Solve the Fractional Nonlinear Partial Differential Equations - Journal of Applied Mathematics and Physics

JAMP > Vol.7 No.4, April 2019

Application of the Improved Kudryashov Method to Solve the Fractional Nonlinear Partial Differential Equations ()

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DOI: 10.4236/jamp.2019.74061 1,013 Downloads 2,626 Views Citations

Author(s)

Md. Abdus Salam¹, Umme Habiba²

Affiliation(s)

¹Department of Mathematics, Mawlana Bhashani Science and Technology University, Tangail, Bangladesh.
²Basic Science Division, World University of Bangladesh, Dhaka, Bangladesh.

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.

KEYWORDS

Improved Kudryashov Method, Time-Space Fractional KdV-Burger Equation, Travelling Wave Solutions, Jumarie’s Modified Riemann-Liouville Derivative

Share and Cite:

Salam, M. and Habiba, U. (2019) Application of the Improved Kudryashov Method to Solve the Fractional Nonlinear Partial Differential Equations. Journal of Applied Mathematics and Physics, 7, 912-920. doi: 10.4236/jamp.2019.74061.

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