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Exact Solutions for Fractional Differential-Difference Equations by (G'/G)-Expansion Method with Modified Riemann-Liouville Derivative

Part of: Random dynamical systems Real functions Miscellaneous topics - Partial differential equations General theory in ordinary differential equations Equations of mathematical physics and other areas of application

Published online by Cambridge University Press:  27 January 2016

Ahmet Bekir ,
Ozkan Guner ,
Burcu Ayhan  and
Adem C. Cevikel
Ahmet Bekir*
Affiliation:
Eskisehir Osmangazi University, Art-Science Faculty, Department of Mathematics-Computer, Eskisehir-Turkey
Ozkan Guner
Affiliation:
Cankiri Karatekin University, Faculty of Economics and Administrative Sciences, Department of International Trade, Cankiri-Turkey
Burcu Ayhan
Affiliation:
Eskisehir Osmangazi University, Art-Science Faculty, Department of Mathematics-Computer, Eskisehir-Turkey
Adem C. Cevikel
Affiliation:
Yildiz Technical University, Education Faculty, Department of Mathematics Education, İstanbul-Turkey
*
*Corresponding author. Email: abekir@ogu.edu.tr (A. Bekir), ozkanguner@karatekin.edu.tr (O. Guner), burcu_ayhan87@hotmail.com (B. Ayhan), acevikel@yildiz.edu.tr (A. C. Cevikel)
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Abstract

In this paper, the (G'/G)-expansion method is suggested to establish new exact solutions for fractional differential-difference equations in the sense of modified Riemann-Liouville derivative. The fractional complex transform is proposed to convert a fractional partial differential difference equation into its differential difference equation of integer order. With the aid of symbolic computation, we choose nonlinear lattice equations to illustrate the validity and advantages of the algorithm. It is shown that the proposed algorithm is effective and can be used for many other nonlinear lattice equations in mathematical physics and applied mathematics.

Keywords

(G'/G)-expansion methodfractional Hybrid Lattice equationfractional modified Korteweg-de Vries equationmodified Riemann-Liouville derivative

MSC classification

Secondary: 34A08: Fractional differential equations 35R11: Fractional partial differential equations 37H10: Generation, random and stochastic difference and differential equations 26A33: Fractional derivatives and integrals 35Q68: PDEs in connection with computer science
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 8 , Issue 2 , April 2016 , pp. 293 - 305
Copyright
Copyright © Global-Science Press 2016 

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