New exact solutions of the conformable space-time two-mode foam drainage equation by two effective methods

SAĞLAM ÖZKAN Y.

Nonlinear Dynamics, 2024 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Publication Date: 2024
  • Doi Number: 10.1007/s11071-024-10010-5
  • Journal Name: Nonlinear Dynamics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Compendex, Computer & Applied Sciences, INSPEC, Metadex, zbMATH, Civil Engineering Abstracts
  • Keywords: Conformable space-time two-mode foam drainage equation, The generalized exponential rational function method (GERFM), The improved version of the Bernoulli sub-equation function method (IBSEFM)
  • Bursa Uludag University Affiliated: Yes

Abstract

In this article, the two-mode foam drainage equation in terms of time and space conformable sense has been investigated. Two effective methods, the generalized exponential rational function method (GERFM) and the improved version of the Bernoulli sub-equation function method (IBSEFM), are used to get new solutions of underlying equation. The fractional travelling wave transformation is applied to convert nonlinear partial differential equations to nonlinear ordinary differential equations. Proposed methods successfully extract trigonometric, hyperbolic and exponential solutions. Some of the obtained solutions are visualized to understand the effect of fractional orders of time and space derivatives on the wave profile and the dynamic behavior of the solutions.