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Existence, Uniqueness and Stability Analysis with the Multiple Exp Function Method for NPDEs

Author

Listed:
  • Safoura Rezaei Aderyani

    (School of Mathematics, Iran University of Science and Technology, Narmak, Tehran 13114-16846, Iran)

  • Reza Saadati

    (School of Mathematics, Iran University of Science and Technology, Narmak, Tehran 13114-16846, Iran)

  • Donal O’Regan

    (School of Mathematical and Statistical Sciences, National University of Ireland, Galway, University Road, H91 TK33 Galway, Ireland)

  • Fehaid Salem Alshammari

    (Department of Mathematics and Statistics, Faculty of Science, Imam Mohammad Ibn Saud Islamic University, Riyadh 11432, Saudi Arabia)

Abstract

In this study, firstly, through an alternative theorem, we study the existence and uniqueness of solution of some nonlinear PDEs and then investigate the Ulam–Hyers–Rassias stability of solution. Secondly, we apply a relatively novel analytical technique, the multiple exp function method, to obtain the multiple wave solutions of presented nonlinear equations. Finally, we propose the numerical results on tables and discuss the advantages and disadvantages of the method.

Suggested Citation

  • Safoura Rezaei Aderyani & Reza Saadati & Donal O’Regan & Fehaid Salem Alshammari, 2022. "Existence, Uniqueness and Stability Analysis with the Multiple Exp Function Method for NPDEs," Mathematics, MDPI, vol. 10(21), pages 1-27, November.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:21:p:4151-:d:964954
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