Differential Transform Method with Complex Transforms to Some Nonlinear Fractional Problems in Mathematical Physics

This paper witnesses the coupling of an analytical series expansion method which is called reduced differential transform with fractional complex transform. The proposed technique is applied on three mathematical models, namely, fractional Kaup-Kupershmidt equation, generalized fractional Drinfeld-S...

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Bibliographic Details
Published in:Mathematical problems in engineering 2015-01, Vol.2015 (2015), p.1-9
Main Authors: Hassan, Saleh M., Ahmad, Jamshad, Awan, Farah Jabeen, Mohyud-Din, Syed Tauseef
Format: Article
Language:English
Subjects:
Acoustics
Coupling
Derivatives
Differential equations
Discretization
Fractional calculus
Initial conditions
Joining
Lagrange multiplier
Mathematical analysis
Mathematical models
Mathematical problems
Nonlinear equations
Partial differential equations
Physics
Polynomials
Power series
Series expansion
Transforms
Water waves
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Summary:This paper witnesses the coupling of an analytical series expansion method which is called reduced differential transform with fractional complex transform. The proposed technique is applied on three mathematical models, namely, fractional Kaup-Kupershmidt equation, generalized fractional Drinfeld-Sokolov equations, and system of coupled fractional Sine-Gordon equations subject to the appropriate initial conditions which arise frequently in mathematical physics. The derivatives are defined in Jumarie’s sense. The accuracy, efficiency, and convergence of the proposed technique are demonstrated through the numerical examples. It is observed that the presented coupling is an alternative approach to overcome the demerit of complex calculation of fractional differential equations. The proposed technique is independent of complexities arising in the calculation of Lagrange multipliers, Adomian’s polynomials, linearization, discretization, perturbation, and unrealistic assumptions and hence gives the solution in the form of convergent power series with elegantly computed components. All the examples show that the proposed combination is a powerful mathematical tool to solve other nonlinear equations also.
ISSN:1024-123X
1563-5147
DOI:10.1155/2015/364853