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Abstract

This paper considers the nonlinear homogeneous fractional Burger's equation as a type of nonlinear fractional partial differential equations (FPDE). Our goal in this paper is to show that an initial value problem (IVP) can be modified with a second initial condition when (α ∈ ( 1,2 ]) as the velocity of the movement, and the obtained solution agrees with the nature of the wave with space and time for the problem. The Caputo fractional derivative is used in all the fractional derivatives. Also, the algorithm of the Laplace transform decomposition method (LTDM) for fractional PDEs is presented. The approximate solution converges to the exact solution in Theorem 1. Also, a numerical simulation is made to confirm the theoretical results. In addition, the solution is displayed graphically for three values of (α ) that belong to the interval ( 1,2 ] to study the effects of changing the value of the fractional order derivative on the wave solutions of the time-fractional Burger PDE. The time interval is extended in each graph to check the effect of time on the number and shape of the waves in addition to changing the fractional order. Finally, a comparison of the obtained solutions is made.

Keywords

Burger's equation, Caputo fractional derivative, Initial value problem, Laplace decomposition method, Mittag-Leffler function

Subject Area

Mathematics

Article Type

Article

First Page

1241

Last Page

1254

Creative Commons License

Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.

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