Solutions of nonlinear fractional coupled Hirota-Satsuma-KdV Equation
DOI:
https://doi.org/10.24297/jam.v13i3.6176Keywords:
nonlinear fractional coupled Hirota-Satsuma-KdV Equation, fractional power series method, Caputo fractional derivativeAbstract
Our interest in the present work is in implementing the FPSM to stress it power in handing the nonlinear fractional coupled Hirota-Satsuma-KdV Equation. The approximate analytical solution of this type equations are obtained.
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References
[1] Ganji, D. D., and M. Rafei. "Solitary wave solutions for a generalized Hirota–Satsuma coupled KdV equation by homotopy perturbation method." Physics Letters A 356.2(2006):131-137.
[2] Abazari, Reza, and M. Abazari. "Numerical simulation of generalized Hirota–Satsuma coupled KdV equation by RDTM and comparison with DTM." Communications in Nonlinear Science & Numerical Simulation17.2(2012):619-629.
[3] Liu, Jincun, and H. Li. "Approximate Analytic Solutions of Time-Fractional Hirota-Satsuma Coupled KdV Equation and Coupled MKdV Equation." Abstract and Applied Analysis,2013,(2013-3-24)2013.2013(2013):103-128.
[4] Seadawy, A. R. "The Solutions of the Boussinesq and Generalized Fifth-Order KdV Equations by Using the Direct Algebraic Method." Applied Mathematical Sciences 6.82(2012):4081-4090.
[5] Yan, Wang Ji, and W. X. Ren. "A direct algebraic method to calculate the sensitivity of element modal strain energy." International Journal for Numerical Methods in Biomedical Engineering 27.5(2011):694–710.
[6] Parkes, E. J., B. R. Duffy, and P. C. Abbott. "The Jacobi elliptic-function method for finding periodic-wave solutions to nonlinear evolution equations." Physics Letters A 295.5–6(2002):280-286.
[7] Ali, A. H. A. "The modified extended tanh-function method for solving coupled MKdV and coupled Hirota–Satsuma coupled KdV equations."Physics Letters A 363.5–6(2007):420-425.
[8] He, Ji Huan. "Variational iteration method – a kind of non-linear analytical technique: some examples." International Journal of Non-Linear Mechanics 34.4(1999):699-708.
[9] Chowdhury, Md., A comparison between the modified homotopy perturbation method and adomian decomposition method for solving nonlinear heat transfer equations, Journal of Applied Sciences, 11 (2011),7, pp.1416-1420.
[10] He, Ji Huan. "Homotopy perturbation method: a new nonlinear analytical technique " Applied Mathematics & Computation 135.1(2003):73–79.
[11] Ray, Santanu Saha. "A new approach for the application of Adomian decomposition method for the solution of fractional space diffusion equation with insulated ends." Applied Mathematics & Computation202.2(2008):544-549.
[12] Wazwaz, Abdul Majid. "The sine–cosine method for obtaining solutions with compact and noncompact structures." Applied Mathematics & Computation 159.2(2004):559-576.
[13] Liao, Shijun, Homotopy analysis method: a new analytical technique for nonlinear problems, Communications in Nonlinear Science and Numerical Simulation, 2 (1997),2, pp.95-100.
[14] Arikoglu, Aytac, and I. Ozkol. "Solution of fractional differential equations by using differential transform method." Chaos Solitons & Fractals34.5(2007):1473-1481.
[15] Kurulay, Muhammet, and M. Bayram. "Power series method for linear partial differential equations of fractional order." Commun.math.appl1.2(2013):71-76.
[16] Hilfer, Rudolf, ed., Applications of fractional calculus in physics, World Scientific, 2000.
[2] Abazari, Reza, and M. Abazari. "Numerical simulation of generalized Hirota–Satsuma coupled KdV equation by RDTM and comparison with DTM." Communications in Nonlinear Science & Numerical Simulation17.2(2012):619-629.
[3] Liu, Jincun, and H. Li. "Approximate Analytic Solutions of Time-Fractional Hirota-Satsuma Coupled KdV Equation and Coupled MKdV Equation." Abstract and Applied Analysis,2013,(2013-3-24)2013.2013(2013):103-128.
[4] Seadawy, A. R. "The Solutions of the Boussinesq and Generalized Fifth-Order KdV Equations by Using the Direct Algebraic Method." Applied Mathematical Sciences 6.82(2012):4081-4090.
[5] Yan, Wang Ji, and W. X. Ren. "A direct algebraic method to calculate the sensitivity of element modal strain energy." International Journal for Numerical Methods in Biomedical Engineering 27.5(2011):694–710.
[6] Parkes, E. J., B. R. Duffy, and P. C. Abbott. "The Jacobi elliptic-function method for finding periodic-wave solutions to nonlinear evolution equations." Physics Letters A 295.5–6(2002):280-286.
[7] Ali, A. H. A. "The modified extended tanh-function method for solving coupled MKdV and coupled Hirota–Satsuma coupled KdV equations."Physics Letters A 363.5–6(2007):420-425.
[8] He, Ji Huan. "Variational iteration method – a kind of non-linear analytical technique: some examples." International Journal of Non-Linear Mechanics 34.4(1999):699-708.
[9] Chowdhury, Md., A comparison between the modified homotopy perturbation method and adomian decomposition method for solving nonlinear heat transfer equations, Journal of Applied Sciences, 11 (2011),7, pp.1416-1420.
[10] He, Ji Huan. "Homotopy perturbation method: a new nonlinear analytical technique " Applied Mathematics & Computation 135.1(2003):73–79.
[11] Ray, Santanu Saha. "A new approach for the application of Adomian decomposition method for the solution of fractional space diffusion equation with insulated ends." Applied Mathematics & Computation202.2(2008):544-549.
[12] Wazwaz, Abdul Majid. "The sine–cosine method for obtaining solutions with compact and noncompact structures." Applied Mathematics & Computation 159.2(2004):559-576.
[13] Liao, Shijun, Homotopy analysis method: a new analytical technique for nonlinear problems, Communications in Nonlinear Science and Numerical Simulation, 2 (1997),2, pp.95-100.
[14] Arikoglu, Aytac, and I. Ozkol. "Solution of fractional differential equations by using differential transform method." Chaos Solitons & Fractals34.5(2007):1473-1481.
[15] Kurulay, Muhammet, and M. Bayram. "Power series method for linear partial differential equations of fractional order." Commun.math.appl1.2(2013):71-76.
[16] Hilfer, Rudolf, ed., Applications of fractional calculus in physics, World Scientific, 2000.
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Published
2017-06-30
How to Cite
Cui, R. (2017). Solutions of nonlinear fractional coupled Hirota-Satsuma-KdV Equation. JOURNAL OF ADVANCES IN MATHEMATICS, 13(3), 7238–7243. https://doi.org/10.24297/jam.v13i3.6176
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