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

Exact Solutions for Fractional Differential-Difference Equations by (G′/G)-Expansion Method with Modified Riemann-Liouville Derivative
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Year:    2016

Author:    Ahmet Bekir, Ozkan Guner, Burcu Ayhan, Adem C. Cevikel

Advances in Applied Mathematics and Mechanics, Vol. 8 (2016), Iss. 2 : pp. 293–305

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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.2014.m798

Advances in Applied Mathematics and Mechanics, Vol. 8 (2016), Iss. 2 : pp. 293–305

Published online:    2016-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    13

Keywords:   

Author Details

Ahmet Bekir

Ozkan Guner

Burcu Ayhan

Adem C. Cevikel

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  3. Exploration of new solitons solutions for the Fitzhugh–Nagumo-type equations with conformable derivatives

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    https://doi.org/10.1142/S0217979222501648 [Citations: 23]

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    https://doi.org/10.1142/S0217979223500844 [Citations: 17]

  11. Novel exact and solitary solutions of conformable Huxley equation with three effective methods

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    https://doi.org/10.1016/j.joes.2022.06.010 [Citations: 8]

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  13. Solitary wave solutions of Fitzhugh–Nagumo-type equations with conformable derivatives

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  14. A family of exact travelling wave solutions of (2+1)-dimensional KdV4 equation

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    https://doi.org/10.1063/1.4972601 [Citations: 0]

  15. A simple technique for constructing exact solutions to nonlinear differential equations with conformable fractional derivative

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    https://doi.org/10.1007/s11082-017-1105-5 [Citations: 21]

  16. Multiple scales analysis and travelling wave solutions for KdV type nonlinear evolution equations

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  17. Mechanical Solving a Few Fractional Partial Differential Equations and Discussing the Effects of the Fractional Order

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    https://doi.org/10.1155/2020/3758353 [Citations: 3]

  18. Vector solutions of the coupled discrete conformable fractional nonlinear Schrödinger equations

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    https://doi.org/10.1016/j.ijleo.2022.168859 [Citations: 9]

  19. New solutions for the high-dimensional fractional BLMP equations

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    Journal of Ocean Engineering and Science, Vol. (2022), Iss.

    https://doi.org/10.1016/j.joes.2022.06.023 [Citations: 3]

  20. Optical solutions for the (3+1)-dimensional YTSF equation

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    https://doi.org/10.1007/s11082-023-04787-9 [Citations: 13]

  21. Solitary wave solutions to some nonlinear fractional evolution equations in mathematical physics

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  22. New analytical solutions for conformable fractional PDEs arising in mathematical physics by exp-function method

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  23. Effects of fractional order time derivative on the solitary wave dynamics of the generalized ZK–Burgers equation

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