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Research Article | Open Access

A survey of KdV-CDG equations via nonsingular fractional operators

Ihsan Ullah1, Aman Ullah1, Shabir Ahmad1, Hijaz Ahmad2,3,4( ), Taher A. Nofal5
Department of Mathematics, University of Malakand, Chakdara, Dir Lower, Khyber Pakhtunkhwa, Pakistan
Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon
Near East University, Operational Research Center in Healthcare, Nicosia 99138, TRNC Mersin 10, Turkey
Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, Roma 3900186, Italy
Department of Mathematic, College of Science, Taif University, P. O. Box 11099, Taif 21944, Saudi Arabia
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Abstract

In this article, the Korteweg-de Vries-Caudrey-Dodd-Gibbon (KdV-CDG) equation is explored via a fractional operator. A nonlocal differential operator with a nonsingular kernel is used to study the KdV-CDG equation. Some theoretical features concerned with the existence and uniqueness of the solution, convergence, and Picard-stability of the solution by using the concepts of fixed point theory are discussed. Analytical solutions of the KdV-CDG equation by using the Laplace transformation (LT) associated with the Adomian decomposition method (ADM) are retrieved. The solutions are presented using 3D and surface graphics.

Keywords

KdV-CDG equationLaplace transformAtangana-Baleanu-Caputo operatorfixed point theory
CLC number: 26A33, 35Q53

References

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AIMS Mathematics
Volume 8 Issue 8,
August 2023
Pages 18964-18981
DOI: 10.3934/math.2023966

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Cite this article:
Ullah I, Ullah A, Ahmad S, et al. A survey of KdV-CDG equations via nonsingular fractional operators. AIMS Mathematics, 2023, 8(8): 18964-18981. https://doi.org/10.3934/math.2023966

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Received: 15 February 2023
Revised: 16 April 2023
Accepted: 24 April 2023
Published: 15 August 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)