Multiple closed form solutions to some fractional order nonlinear evolution equations in physics and plasma physics

M. Ali Akbar; Norhashidah Hj. Mohd. Ali; M. Tarikul Islam; M. Ali Akbar; Norhashidah Hj. Mohd. Ali; M. Tarikul Islam

doi:10.3934/math.2019.3.397

AIMS Mathematics

2019, Volume 4, Issue 3: 397-411. doi: 10.3934/math.2019.3.397

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Multiple closed form solutions to some fractional order nonlinear evolution equations in physics and plasma physics

1.
Department of Applied Mathematics, University of Rajshahi, Bangladesh
2.
School of Mathematical Sciences, Universiti Sains Malaysia, Malaysia
3.
Department of Mathematics, Hajee Mohammad Danesh Science and Technology University, Dinajpur, Bangladesh

Received: 30 January 2019 Accepted: 12 April 2019 Published: 23 April 2019

Nonlinear evolution equations (NLEEs) of fractional order play important role to explain the inner mechanisms of complex phenomena in various fields of the real world. In this article, nonlinear evolution equations of fractional order; namely, the (3+1)-dimensional space-time fractional modified KdV-Zakharov-Kuznetsov equation, the time fractional biological population model and the space-time fractional modified regularized long-wave equation are revealed for seeking closed form analytic solutions. The offered equations are first transformed into ordinary differential equations of integer order with the help of a suitable composite transformation and the conformable fractional derivative. Then the rational $(G'/G)$-expansion method, which is reliable, efficient and computationally attractive, is employed to construct the traveling wave solutions successfully. The obtained solutions are appeared to be exact, much more new and general than the existing results in the literature.
Citation: M. Ali Akbar, Norhashidah Hj. Mohd. Ali, M. Tarikul Islam. Multiple closed form solutions to some fractional order nonlinear evolution equations in physics and plasma physics[J]. AIMS Mathematics, 2019, 4(3): 397-411. doi: 10.3934/math.2019.3.397

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Abstract

Nonlinear evolution equations (NLEEs) of fractional order play important role to explain the inner mechanisms of complex phenomena in various fields of the real world. In this article, nonlinear evolution equations of fractional order; namely, the (3+1)-dimensional space-time fractional modified KdV-Zakharov-Kuznetsov equation, the time fractional biological population model and the space-time fractional modified regularized long-wave equation are revealed for seeking closed form analytic solutions. The offered equations are first transformed into ordinary differential equations of integer order with the help of a suitable composite transformation and the conformable fractional derivative. Then the rational $(G'/G)$-expansion method, which is reliable, efficient and computationally attractive, is employed to construct the traveling wave solutions successfully. The obtained solutions are appeared to be exact, much more new and general than the existing results in the literature.

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