Abstract
This paper introduces a new approximate-analytical approach for solving systems of Fractional Nonlinear Partial Differential Equations (FNPDEs). However, the main advantage of this new approximate-analytical approach is to obtain the analytical solution for general systems of FNPDEs in forms of convergent series with easily computable components using Caputo fractional partial derivative. Moreover, the convergence theorem and error analysis of the proposed method are also shown. Solitary wave solutions and traveling wave solutions for the system of fractional dispersive wave equations and the system of fractional long water wave equations are successfully obtained. The numerical solutions are also obtained in forms of tables and graphs to confirm the accuracy and efficiency of the suggested method.
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The authors thank the referees for their valuable suggestions and comments.
Funding
The research by James Peters has been supported by the Natural Sciences & Engineering Research Council of Canada (NSERC) discovery grant 185986, Scientific and Technological Research Council of Turkey (TÜBİTAK) Scientific Human Resources Development (BIDEB) under Grant no: 2221-1059B211402463, and Instituto Nazionale di Alta Matematica (INdAM) Francesco Severi, Gruppo Nazionale per le Strutture Algebriche, Geometriche e Loro Applicazioni grant 9 920160 000362, n.prot U 2016/000036.
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Hayman Thabet and Subhash Kendre contributed substantially to this paper. Hayman Thabet wrote this paper, Subhash Kendre supervised the development of the paper, James Peters and Melike Kaplan helped in evaluating and editing the paper.
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Communicated by Agnieszka Malinowska.
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Thabet, H., Kendre, S., Peters, J. et al. Solitary wave solutions and traveling wave solutions for systems of time-fractional nonlinear wave equations via an analytical approach. Comp. Appl. Math. 39, 144 (2020). https://doi.org/10.1007/s40314-020-01163-1
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DOI: https://doi.org/10.1007/s40314-020-01163-1
Keywords
- New approximate-analytical approach
- Systems of fractional nonlinear partial differential equations
- Systems of time-fractional nonlinear wave equations
- Solitary wave solutions
- Traveling wave solutions