Abstract
In this paper, the new mapping approach and the new extended auxiliary equation approach were used to investigate the exact traveling wave solutions of (2 + 1)-dimensional time-fractional Zoomeron equation with the conformable fractional derivative. As a result, the singular soliton solutions, kink and anti-kink soliton solutions, periodic function soliton solutions, Jacobi elliptic function solutions and hyperbolic function solutions of (2 + 1)-dimensional time-fractional Zoomeron equation were obtained. Finally, the 3D and 2D graphs of some solutions were drawn by setting the suitable values of parameters with Maple, and analyze the dynamic behaviors of the solutions.
Highlights
Fractional partial differential equations (FPDEs) have a wide of applications in different fields, such as biology, physics, signal processing, fluid mechanics, and electromagnetic, and so on
Inspired by the reference [22], we introduce the new mapping approach and the new extended auxiliary equation approach [23] [24] [25] to investigate the exact solutions of (2 + 1)-dimensional timefractional Zoomeron equation [20]:
The organization of this paper is as follows: In Section 2, we introduce the conformable fractional derivative
Summary
Fractional partial differential equations (FPDEs) have a wide of applications in different fields, such as biology, physics, signal processing, fluid mechanics, and electromagnetic, and so on. Many effective methods have been presented to obtain the exact traveling wave solutions of FPDEs, for example,. + 1)-dimensional conformable time-fractional Zoomeron equation into ordinary differential equation. Inspired by the reference [22], we introduce the new mapping approach and the new extended auxiliary equation approach [23] [24] [25] to investigate the exact solutions of (2 + 1)-dimensional timefractional Zoomeron equation [20]:. [21] obtained new exact solutions of Equation (1) by using the auxiliary equation method.
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