Novel Exact Soliton Solutions of Cahn–Allen Models with Truncated M-fractional Derivative
Mohammad Mobarak Hossain,
Md. Mamunur Roshid,
Md. Abu Naim Sheikh,
Mohammad Abu Taher,
Harun-Or-Roshid
Issue:
Volume 8, Issue 6, December 2022
Pages:
112-120
Received:
20 September 2022
Accepted:
7 November 2022
Published:
29 December 2022
DOI:
10.11648/j.ijtam.20220806.11
Downloads:
Views:
Abstract: In recent research the effect of different type fractional derivative to nonlinear evolution equations plays a vital rule in the various branches of science and engineering. The nonlinear physical phenomena are expressed by nonlinear partial differential equations which are characteristics on the field of solid-state physics, plasma physics, fluid mechanics, chemical physics, mechanics, biology, chemistry, and so on. To visualize and identify their properties, it is essential to find the exact and multi solitons of the related nonlinear partial differential equation. In this work, we investigate more soliton solutions for novel truncated M-fractional Cahn–Allen (t-MfCA) models to secure different soliton solutions via the unified scheme. This model has significant in the area of mathematical physics and also known as reaction–diffusion. The obtained solutions are expressed in turns of trigonometric, hyperbolic and rational function solution under the condition on the free constraints. This work offers the kink, singular soliton, different type interaction of kink and lump wave for the numerical value of the free constraints. Form the obtained solution it is shown that the implement method is more informal, effective and reliable as compared to other methods. The calculation and all analytic solutions are verified by computational software MAPLE 18.
Abstract: In recent research the effect of different type fractional derivative to nonlinear evolution equations plays a vital rule in the various branches of science and engineering. The nonlinear physical phenomena are expressed by nonlinear partial differential equations which are characteristics on the field of solid-state physics, plasma physics, fluid ...
Show More
defined by a third kind linear singular integral equation in some generalized functional spaces. The extended operator A of the initial noether operator A is verified being also noether and therefore we deduce the index of the extended operator