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# Application of the Exp-Function and Generalized Kudryashov Methods for Obtaining New Exact Solutions of Certain Nonlinear Conformable Time Partial Integro-Differential Equations

by 1,2,* and
1
Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand
2
Centre of Excellence in Mathematics, CHE, Si Ayutthaya Road, Bangkok 10400, Thailand
*
Author to whom correspondence should be addressed.
Academic Editors: Yongwimon Lenbury, Ravi P. Agarwal, Philip Broadbridge, Dongwoo Sheen and Shan Zhao
Computation 2021, 9(5), 52; https://doi.org/10.3390/computation9050052
Received: 25 March 2021 / Revised: 16 April 2021 / Accepted: 23 April 2021 / Published: 26 April 2021
The key objective of this paper is to construct exact traveling wave solutions of the conformable time second integro-differential Kadomtsev–Petviashvili (KP) hierarchy equation using the Exp-function method and the (2 + 1)-dimensional conformable time partial integro-differential Jaulent–Miodek (JM) evolution equation utilizing the generalized Kudryashov method. These two problems involve the conformable partial derivative with respect to time. Initially, the conformable time partial integro-differential equations can be converted into nonlinear ordinary differential equations via a fractional complex transformation. The resulting equations are then analytically solved via the corresponding methods. As a result, the explicit exact solutions for these two equations can be expressed in terms of exponential functions. Setting some specific parameter values and varying values of the fractional order in the equations, their 3D, 2D, and contour solutions are graphically shown and physically characterized as, for instance, a bell-shaped solitary wave solution, a kink-type solution, and a singular multiple-soliton solution. To the best of the authors’ knowledge, the results of the equations obtained using the proposed methods are novel and reported here for the first time. The methods are simple, very powerful, and reliable for solving other nonlinear conformable time partial integro-differential equations arising in many applications. View Full-Text
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MDPI and ACS Style

Kaewta, S.; Sirisubtawee, S.; Sungnul, S. Application of the Exp-Function and Generalized Kudryashov Methods for Obtaining New Exact Solutions of Certain Nonlinear Conformable Time Partial Integro-Differential Equations. Computation 2021, 9, 52. https://doi.org/10.3390/computation9050052

AMA Style

Kaewta S, Sirisubtawee S, Sungnul S. Application of the Exp-Function and Generalized Kudryashov Methods for Obtaining New Exact Solutions of Certain Nonlinear Conformable Time Partial Integro-Differential Equations. Computation. 2021; 9(5):52. https://doi.org/10.3390/computation9050052

Chicago/Turabian Style

Kaewta, Supaporn, Sekson Sirisubtawee, and Surattana Sungnul. 2021. "Application of the Exp-Function and Generalized Kudryashov Methods for Obtaining New Exact Solutions of Certain Nonlinear Conformable Time Partial Integro-Differential Equations" Computation 9, no. 5: 52. https://doi.org/10.3390/computation9050052

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