Abstract
AbstractIn 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.
Publisher
Springer Science and Business Media LLC
Reference72 articles.
1. Rezazadeh, H., Inc, M., Baleanu, D.: New solitary wave solutions for variants of (3+ 1)-dimensional Wazwaz-Benjamin-Bona-Mahony equations. Front. Phys. 8, 332 (2020)
2. Rehman, H.U., Iqbal, I., Subhi Aiadi, S., Mlaiki, N., Saleem, M.S.: Soliton solutions of Klein-Fock-Gordon equation using Sardar subequation method. Mathematics 10(18), 3377 (2022)
3. Tozar, A., Kurt, A., Tasbozan, O.: New wave solutions of an integrable dispersive wave equation with a fractional time derivative arising in ocean engineering models. Kuwait J. Sci. 47(2), 22–33 (2020)
4. Rezazadeh, H.: New solitons solutions of the complex Ginzburg-Landau equation with Kerr law nonlinearity. Optik 167, 218–227 (2018)
5. Behera, S., Virdi, J.P.S.: Some more solitary travelling wave solutions of nonlinear evolution equations. Discontin. Nonlinearity, Complex. 12(01), 75–85 (2023)