Exact Solutions for the Sharma–Tasso–Olver Equation via the Sardar Subequation Method with a Comparison between Atangana Space–Time Beta-Derivatives and Classical Derivatives

Chanidaporn Pleumpreedaporn, Elvin J. Moore (), Sekson Sirisubtawee, Nattawut Khansai and Songkran Pleumpreedaporn
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Chanidaporn Pleumpreedaporn: Department of Mathematics, Faculty of Science and Technology, Rambhai Barni Rajabhat University, Chanthaburi 22000, Thailand
Elvin J. Moore: Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand
Sekson Sirisubtawee: Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand
Nattawut Khansai: Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand
Songkran Pleumpreedaporn: Department of Mathematics, Faculty of Science and Technology, Rambhai Barni Rajabhat University, Chanthaburi 22000, Thailand

Mathematics, 2024, vol. 12, issue 14, 1-15

Abstract: The Sharma–Tasso–Olver (STO) equation is a nonlinear, double-dispersive, partial differential equation that is physically important because it provides insights into the behavior of nonlinear waves and solitons in various physical areas, including fluid dynamics, optical fibers, and plasma physics. In this paper, the STO equation is generalized to a fractional equation by using Atangana (or Atangana–Baleanu) fractional space and time beta-derivatives since they have been found to be useful as a model for a variety of traveling-wave phenomena. Exact solutions are obtained for the integer-order and fractional-order equations by using the Sardar subequation method and an appropriate traveling-wave transformation. The exact solutions are obtained in terms of generalized trigonometric and hyperbolic functions. The exact solutions are derived for the integer-order STO and for a range of values of fractional orders. Numerical solutions are also obtained for a range of parameter values for both the fractional and integer orders to show some of the types of solutions that can occur. As examples, the solutions are obtained showing the physical behavior, such as the solitary wave solutions of the singular kink-type and periodic wave solutions. The results show that the Sardar subequation method provides a straightforward and efficient method for deriving new exact solutions for fractional nonlinear partial differential equations of the STO type.

Keywords: dispersive equation; fractional beta-derivative; traveling wave; soliton; kink-type solution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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