Traveling wave solutions in closed form for some nonlinear fractional evolution equations related to conformable fractional derivative

M. TarikulIslam; M. AliAkbar; M. Abul Kalam Azad; M. TarikulIslam; M. AliAkbar; M. Abul Kalam Azad

doi:10.3934/Math.2018.4.625

AIMS Mathematics

2018, Volume 3, Issue 4: 625-646. doi: 10.3934/Math.2018.4.625

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Research article

Traveling wave solutions in closed form for some nonlinear fractional evolution equations related to conformable fractional derivative

1.
Department of Mathematics, Hajee Mohammad Danesh Science and Technology University, Dinajpur, Bangladesh
2.
Department of Applied Mathematics, Rajshahi University, Rajshahi, Bangladesh

Received: 15 October 2018 Accepted: 27 November 2018 Published: 17 December 2018
MSC : 34A08, 35R11

Fractional order nonlinear evolution equations involving conformable fractional derivative are formulated and revealed for attractive solutions to depict the physical phenomena of nonlinear mechanisms in the real world. The core aim of this article is to explore further new general exact traveling wave solutions of nonlinear fractional evolution equations, namely, the space time fractional (2+1)-dimensional dispersive long wave equations, the (3+1)-dimensional space time fractional mKdV-ZK equation and the space time fractional modified regularized long-wave equation. The mentioned equations are firstly turned into the fractional order ordinary differential equations with the aid of a suitable composite transformation and then hunted their solutions by means of recently established fractional generalized $\left({D_\xi ^\alpha G/G} \right)$-expansion method. This productive method successfully generates many new and general closed form traveling wave solutions in accurate, reliable and efficient way in terms of hyperbolic, trigonometric and rational. The obtained results might play important roles for describing the complex phenomena related to science and engineering and also be newly recorded in the literature for their high acceptance. The suggested method will draw the attention to the researchers to establish further new solutions to any other nonlinear evolution equations.
Citation: M. TarikulIslam, M. AliAkbar, M. Abul Kalam Azad. Traveling wave solutions in closed form for some nonlinear fractional evolution equations related to conformable fractional derivative[J]. AIMS Mathematics, 2018, 3(4): 625-646. doi: 10.3934/Math.2018.4.625

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Abstract

Fractional order nonlinear evolution equations involving conformable fractional derivative are formulated and revealed for attractive solutions to depict the physical phenomena of nonlinear mechanisms in the real world. The core aim of this article is to explore further new general exact traveling wave solutions of nonlinear fractional evolution equations, namely, the space time fractional (2+1)-dimensional dispersive long wave equations, the (3+1)-dimensional space time fractional mKdV-ZK equation and the space time fractional modified regularized long-wave equation. The mentioned equations are firstly turned into the fractional order ordinary differential equations with the aid of a suitable composite transformation and then hunted their solutions by means of recently established fractional generalized $\left({D_\xi ^\alpha G/G} \right)$-expansion method. This productive method successfully generates many new and general closed form traveling wave solutions in accurate, reliable and efficient way in terms of hyperbolic, trigonometric and rational. The obtained results might play important roles for describing the complex phenomena related to science and engineering and also be newly recorded in the literature for their high acceptance. The suggested method will draw the attention to the researchers to establish further new solutions to any other nonlinear evolution equations.

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