Diverse Precise Traveling Wave Solutions Possessing Beta Derivative of the Fractional Differential Equations Arising in Mathematical Physics

In this paper, we obtain the novel exact traveling wave solutions in the form of trigonometric, hyperbolic and exponential functions for the nonlinear time fractional generalized reaction Duffing model and density dependent fractional diffusion-reaction equation in the sense of beta-derivative by us...

Full description

Saved in:
Bibliographic Details
Main Authors: Imran Siddique, Arshad M. Mirza, Kausar Shahzadi, M. Ali Akbar, Fahd Jarad
Format: Article
Language:English
Published: Wiley 2022-01-01
Series:Journal of Function Spaces
Online Access:http://dx.doi.org/10.1155/2022/5613708
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1832562214694813696
author Imran Siddique
Arshad M. Mirza
Kausar Shahzadi
M. Ali Akbar
Fahd Jarad
author_facet Imran Siddique
Arshad M. Mirza
Kausar Shahzadi
M. Ali Akbar
Fahd Jarad
author_sort Imran Siddique
collection DOAJ
description In this paper, we obtain the novel exact traveling wave solutions in the form of trigonometric, hyperbolic and exponential functions for the nonlinear time fractional generalized reaction Duffing model and density dependent fractional diffusion-reaction equation in the sense of beta-derivative by using three fertile methods, namely, Generalized tanh (GT) method, Generalized Bernoulli (GB) sub-ODE method, and Riccati-Bernoulli (RB) sub-ODE method. The derived solutions to the aforementioned equations are validated through symbolic soft computations. To promote the vital propagated features; some investigated solutions are exhibited in the form of 2D and 3D graphics by passing on the specific values to the parameters under the confine conditions. The accomplished solutions show that the presented methods are not only powerful mathematical tools for generating more solutions of nonlinear time fractional partial differential equations but also can be applied to nonlinear space-time fractional partial differential equations.
format Article
id doaj-art-c247109123e94322bfc4db80e1807837
institution Kabale University
issn 2314-8888
language English
publishDate 2022-01-01
publisher Wiley
record_format Article
series Journal of Function Spaces
spelling doaj-art-c247109123e94322bfc4db80e18078372025-02-03T01:23:15ZengWileyJournal of Function Spaces2314-88882022-01-01202210.1155/2022/5613708Diverse Precise Traveling Wave Solutions Possessing Beta Derivative of the Fractional Differential Equations Arising in Mathematical PhysicsImran Siddique0Arshad M. Mirza1Kausar Shahzadi2M. Ali Akbar3Fahd Jarad4Department of MathematicsDepartment of PhysicsDepartment of MathematicsDepartment of Applied MathematicsDepartment of MathematicsIn this paper, we obtain the novel exact traveling wave solutions in the form of trigonometric, hyperbolic and exponential functions for the nonlinear time fractional generalized reaction Duffing model and density dependent fractional diffusion-reaction equation in the sense of beta-derivative by using three fertile methods, namely, Generalized tanh (GT) method, Generalized Bernoulli (GB) sub-ODE method, and Riccati-Bernoulli (RB) sub-ODE method. The derived solutions to the aforementioned equations are validated through symbolic soft computations. To promote the vital propagated features; some investigated solutions are exhibited in the form of 2D and 3D graphics by passing on the specific values to the parameters under the confine conditions. The accomplished solutions show that the presented methods are not only powerful mathematical tools for generating more solutions of nonlinear time fractional partial differential equations but also can be applied to nonlinear space-time fractional partial differential equations.http://dx.doi.org/10.1155/2022/5613708
spellingShingle Imran Siddique
Arshad M. Mirza
Kausar Shahzadi
M. Ali Akbar
Fahd Jarad
Diverse Precise Traveling Wave Solutions Possessing Beta Derivative of the Fractional Differential Equations Arising in Mathematical Physics
Journal of Function Spaces
title Diverse Precise Traveling Wave Solutions Possessing Beta Derivative of the Fractional Differential Equations Arising in Mathematical Physics
title_full Diverse Precise Traveling Wave Solutions Possessing Beta Derivative of the Fractional Differential Equations Arising in Mathematical Physics
title_fullStr Diverse Precise Traveling Wave Solutions Possessing Beta Derivative of the Fractional Differential Equations Arising in Mathematical Physics
title_full_unstemmed Diverse Precise Traveling Wave Solutions Possessing Beta Derivative of the Fractional Differential Equations Arising in Mathematical Physics
title_short Diverse Precise Traveling Wave Solutions Possessing Beta Derivative of the Fractional Differential Equations Arising in Mathematical Physics
title_sort diverse precise traveling wave solutions possessing beta derivative of the fractional differential equations arising in mathematical physics
url http://dx.doi.org/10.1155/2022/5613708
work_keys_str_mv AT imransiddique diverseprecisetravelingwavesolutionspossessingbetaderivativeofthefractionaldifferentialequationsarisinginmathematicalphysics
AT arshadmmirza diverseprecisetravelingwavesolutionspossessingbetaderivativeofthefractionaldifferentialequationsarisinginmathematicalphysics
AT kausarshahzadi diverseprecisetravelingwavesolutionspossessingbetaderivativeofthefractionaldifferentialequationsarisinginmathematicalphysics
AT maliakbar diverseprecisetravelingwavesolutionspossessingbetaderivativeofthefractionaldifferentialequationsarisinginmathematicalphysics
AT fahdjarad diverseprecisetravelingwavesolutionspossessingbetaderivativeofthefractionaldifferentialequationsarisinginmathematicalphysics