The generalized Kudryashov method for nonlinear space–time fractional partial differential equations of Burgers type

The nonlinear space–time fractional differential equations (FDE) of Burgers’ type play an important role for describing many phenomena in applied sciences. This paper develops a generalized version of the modified Kudryashov method to obtain the exact solutions for FDE of Burgers’ type. The FDE are...

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Bibliographic Details
Published in:Nonlinear dynamics 2019, Vol.95 (1), p.361-368
Main Authors: Gaber, A. A., Aljohani, A. F., Ebaid, A., Machado, J. Tenreiro
Format: Article
Language:English
Subjects:
Automotive Engineering
Classical Mechanics
Control
Dynamical Systems
Engineering
Exact solutions
Fractional calculus
Mathematical analysis
Mechanical Engineering
Ordinary differential equations
Original Paper
Partial differential equations
Traveling waves
Vibration
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Summary:The nonlinear space–time fractional differential equations (FDE) of Burgers’ type play an important role for describing many phenomena in applied sciences. This paper develops a generalized version of the modified Kudryashov method to obtain the exact solutions for FDE of Burgers’ type. The FDE are firstly reduced to a set of ordinary differential equations by means of a fractional complex transformation and, afterward, they are solved by applying the generalized Kudryashov method (GKM). Several kinds of traveling wave solutions such as kink and singular kink waves are illustrated with various figures and discussed. The results demonstrate the efficiency of the GKM in tackling space–time partial FDE.
ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-018-4568-4