Analytical Solutions for Nonlinear Systems of Conformable Space-Time Fractional Partial Differential Equations via Generalized Fractional Differential Transform
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The present paper introduces approximate analytical solutions for nonlinear systems of conformable space-time fractional partial differential equations (CSTFPDEs) by using a generalized conformable fractional partial differential transform (GCFPDT). The GCFPDT is a modified version of the conformable fractional partial differential transform introduced in our recent work and it can be used as an efficient alternative transform to find analytical solutions for nonlinear systems of CSTFPDEs available in the literature. The convergence and error estimation of the proposed GCFPDT are also considered. Moreover, approximate analytical solutions to nonlinear system of gas dynamic equations, nonlinear system of KdV equations, and nonlinear system of approximate long water wave equations in the sense of conformable space-time fractional partial derivatives are successfully obtained to confirm the effectiveness and efficiency of the proposed GCFPDT.
KeywordsNonlinear systems of CSTFPDEs The GCFPDT Convergence Maximum absolute truncated error Nonlinear system of gas dynamic equations System of KdV equations System of approximate long water wave equations
Mathematics Subject Classification (2010)93C10 35R11
The authors thank the referees for their valuable suggestions and comments.
Hayman Thabet and Subhash Kendre contributed substantially to this paper. Hayman Thabet wrote this paper, Subhash Kendre supervised the development of the paper, and James Peters helped evaluate and edit the paper.
The research by Hayman Thabet is supported by Savitribai Phule Pune University (formerly University of Pune), Pune 411007, India. The research by J.F. 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.
- 11.Thabet, H., Kendre, S.: Elementary course in fractional calculus. LAP Lambert Academic Publishing (2018)Google Scholar
- 17.Kilbas, A.A., Srivastava, H.M., Trujillo, J.J.: Theory and applications of fractional differential equations. North-Holland Mathematics Studies, vol. 204. Elsevier, Amsterdam (2006)Google Scholar
- 18.Podlubny, I.: Fractional differential equations: An introduction to fractional derivatives, fractional differential equations to methods of their solution and some of their applications. Mathematics in Science and Engineering, vol. 198. Academic Press, San Diego (1998)Google Scholar