THERMAL SCIENCE

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Bo Xu

,

Yue Yu

,

Sheng Zhang

EXACT SOLUTIONS AND NON-LINEAR ADAPTIVE BOUNDARY CONTROL PROBLEM OF THE FRACTIONAL MODIFIED GENERALIZED KDV-BURGERS EQUATION

ABSTRACT
This article extends a modified generalized KdV-Burgers equation to the conformable fractional version with the aim of exploring novel solution structures and non-linear adaptive boundary control problems for fractional-order models. The results obtained include hyperbolic functional solutions of the fractional modified generalized KdV-Burgers equation and a non-linear adaptive boundary control law designed by attaching initial and boundary value conditions. It is demonstrated that the obtained hyperbolic functional solutions exhibit novel spatial structures, and that the solution of the fractional initial and boundary value problem is globally exponential stability.
KEYWORDS
fractional modified generalized KdV-Burgers equation, hyperbolic function solution, initial and boundary value problem, non-linear adaptive boundary control law, auxiliary equation, global exponential stability
PAPER SUBMITTED: 2024-04-27
PAPER REVISED: 2024-05-15
PAPER ACCEPTED: 2024-05-15
PUBLISHED ONLINE: 2025-07-06
DOI REFERENCE: https://doi.org/10.2298/TSCI2503749X
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2025, VOLUME 29, ISSUE Issue 3, PAGES [1749 - 1756]
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Exact solutions and non-linear adaptive boundary control problem of the fractional modified generalized KdV-burgers equation

2025 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence