Analytical Solutions for Nonlinear Systems of Conformable Space-Time Fractional Partial Differential Equations via Generalized Fractional Differential Transform

  • Hayman ThabetEmail author
  • Subhash Kendre
  • James Peters


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.


Nonlinear 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.

Author Contributions

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.

Funding Information

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.


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Copyright information

© Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.Department of MathematicsSavitribai Phule Pune UniversityPuneIndia
  2. 2.Computational Intelligence LaboratoryUniversity of ManitobaWinnipegCanada
  3. 3.Department of Mathematics, Faculty of Arts and ScienceAdıyaman UniversityAdyamanTurkey

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