SOLITARY WAVE SOLUTIONS FOR SPACE-TIME FRACTIONAL COUPLED INTEGRABLE DISPERSIONLESS SYSTEM VIA GENERALIZED KUDRYASHOV METHOD

Ahmed Gaber, Hijaz Ahmad

DOI Number
https://doi.org/10.22190/FUMI2005439G
First page
1439
Last page
1449

Abstract


In this article, space-time fractional coupled integrable dispersionless system is considered, and we use fractional derivative in the sense of modified Riemann-Liouville. The fractional system has reduced to an ordinary differential system by fractional transformation and the generalized Kudryashov method is applied to obtain exact solutions. We also testify performance as well as precision of the applied method by means of numerical tests for obtaining solutions. The obtained results have been graphically presented to show the properties of the solutions.

Keywords

integrable dispersionless system; fractional derivative; differential system.

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References


Zheng Bin, (G'/G)-Expansion Method for Solving Fractional Partial Differential Equations in the Theory of Mathematical Physics, Commun. Theor. Phys. 58 (2012) 623-630.

Mohd. Farman Ali, Manoj Sharma, Renu Jain, An Application of Fractional Calculus in Electrical Engineering, Adv. Eng. Tec. Appl. 5 (2016), 41-45.

N. H. Abel, Solution De Quelques Problems a L'aide D'integrals Denites. Oeuvres Completes, Grondahl Christiania, Norway,1 (1881),16-18.

Mehdi Dalir, Majid Bashour, Applications of Fractional Calculus, App. Math. Sci., (4) (2010), 1021-1032.

Yokus A, Durur H, Ahmad H. Hyperbolic type solutions for the couple Boiti-Leon-Pempinelli system. Facta Universitatis, Series: Mathematics and Informatics. 2020;35(2):523-31.

Yokus A, Durur H, Ahmad H, Yao SW. Construction of Different Types Analytic Solutions for the Zhiber-Shabat Equation. Mathematics. 2020;8(6):908.

Ahmad H, Seadawy AR, Khan TA, Thounthong P. Analytic approximate solutions for some nonlinear Parabolic dynamical wave equations. Journal of Taibah University for Science. 2020;14(1):346-58.

Ahmad H, Khan TA, Stanimirovic PS, Ahmad I. Modied Variational Iteration Technique for the Numerical Solution of Fifth Order KdV Type Equations. Journal of Applied and Computational Mechanics. 2020;6(SI):1220-1227

Kamran Ayub, M. Yaqub Khan, Qazi Mahmood-Ul-Hassan, Solitary and periodic wave solutions of Calogero-Bogoyavlenskii-Schiff equation via exp-function methods, Computers & Math. App., 74 (2017), 3231-3241.

Ahmad, H., Khan, T. A., Ahmad, I., Stanimirović, P. S., Chu, Y.-M., A new analyzing technique for nonlinear time fractional Cauchy reaction-diffusion model equations, Results in Physics, 2020, 103462. doi: https://doi.org/10.1016/j.rinp.2020.103462.

Ahmad, H., Akgul, A., Khan, T. A., Stanimirović, P. S., Chu, Y.-M., New Perspective on the Conventional Solutions of the Nonlinear Time-Fractional Partial Differential Equations, Complexity, 2020,2020, 8829017. doi:10.1155/2020/8829017.

A. A. Gaber, Symmetry analysis and Solitary wave solutions of nonlinear ion-acoustic waves equation. Int. J. Ana. App. 18 (2020) 448-460.

Akgul A. and Ahmad H., Reproducing Kernel Method for Fangzhu^aeTMs Oscillator for Water Collection from Air, Mathematical Methods in the Applied Sciences. 2020, DOI:10.1002/mma.6853

Arzu Akbulut, Melike Kaplan, Auxiliary equation method for time-fractional differential equations with conformable derivative, Comput. & Math. with Appl., 75 (2018), 876-882.

Ahmad, H., Khan, T. A., Stanimirović, P. S., Chu, Y.-M., Ahmad, I., Modied Variational Iteration Algorithm-II: Convergence and Applications to Diffusion Models, Complexity, 2020, 8841718. doi:10.1155/2020/8841718.

Ahmad H, Seadawy AR, Khan TA. Study on numerical solution of dispersive water wave phenomena by using a reliable modication of variational iteration algorithm. Mathematics and Computers in Simulation. 2020;177:13-23

A. A. Gaber and et., The generalized version of Kudryashov method for nonlinear space-time fractional partial differential equations of Burgers type, Nonlinear Dynamics, Nonlinear Dyn. 95 (2019), 361-368.

K. Hosseini, A. Bekir, R. Ansari, New exact solutions of the conformable timefractional Cahn-Allen and Cahn-Hilliard equations using the modied Kudryashov method, Optik,132 (2017), 203-209.

Dipankar Kumar, Aly R. Seadawy, Atish Kumar Joardar, Modied Kudryashov method via new exact solutions for some conformable fractional differential equations arising in mathematical biology, Chinese Journal of Physics, 56 (2018), 75-85.

Abdelhalim Ebaid, Doaa M. M. ElSayed, Fractional Calculus Model for Damped Mathieu Equation Approximate Analytical Solution, App. Math. Sci., 6 (2012), 4075 - 4080.

Amit Prakash, Manoj Kumar, Kapil K. Sharma, Numerical method for solving fractional coupled Burgers equations, App. Math. Comp. 260 (2015) 314-320

R. Sahadevan, P. Prakash, On Lie symmetry analysis and invariant subspace methods of coupled time fractional partial differential equations, Chaos, Solitons &Fractals 104 (2017) 107-120.

Qing Huang, Renat Zhdanov, Symmetries and exact solutions of the time fractional Harry-Dym equation with Riemann{Liouville derivative, Phy. A 409 (2014) 110-118.

Ozkan Guner, Esin Aksoy, Ahmet Bekir, Adem C. Cevikel,Different methods for (3 + 1)-dimensional space-time fractional modied KdV-Zakharov-Kuznetsov equation,

Comp. & Math. with Applications, 71(2016), 1259-1269.

I. Naeem, M.D. Khan, Symmetry classication of time-fractional diffusion equation, Commun Nonlinear Sci Numer Simulat 42 (2017) 560-570.

S. Sahoo, S. Saha Ray, Invariant analysis with conservation laws for the time fractional Drinfeld-Sokolov-Satsuma-Hirota equations,Chaos, Solitons and Fractals 104 (2017) 725{733.

H. Kakuhata and K. Konno, Loop Soliton Solutions of String Interacting with External Field, J. Phys. Soc. Jpn. 68 (1999) 757.

WANG Pan, TIAN Bo, LIU Wen-Jun , QU Qi-Xing, and JIANG Yan, Conservation Laws and Analytic Soliton Solutions for Coupled Integrable Dispersionless Equations with Symbolic Computation.

K. Konno and H. Oono, New Coupled Integrable Dispersionless Equations, J. Phys. Soc. Jpn. 63 (1994) 377.

DAI Chao-Qing, YANG Qin, and WANG Yue-Yue, New Exact Solutions of (1 + 1)-Dimensional Coupled Integrable Dispersionless System, Commun. Theor. Phys. 55 (2011) 622{628.

A.Y.T. Leung, H.X. Yang, Z.J. Guo, Periodic wave solutions of coupled integrable dispersionless equations by residue harmonic balance, Commun Nonlinear Sci Numer Simulat 17 (2012) 4508{4514.

A. Ebaid, An improvement on the Exp-function method when balancing the highest order linear and nonlinear terms, J. Math. Anal. Appl. 392 (2012) 1-5.




DOI: https://doi.org/10.22190/FUMI2005439G

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