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

Safoura Rezaei Aderyani, Reza Saadati (), Donal O’Regan and Fehaid Salem Alshammari
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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

Mathematics, 2022, vol. 10, issue 21, 1-27

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.

Keywords: multiple exp-function method; analytical method; NPDE; fixed point method; UHRS (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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