A survey of KdV-CDG equations via nonsingular fractional operators

Ihsan Ullah; Aman Ullah; Shabir Ahmad; Hijaz Ahmad; Taher A. Nofal; Ihsan Ullah; Aman Ullah; Shabir Ahmad; Hijaz Ahmad; Taher A. Nofal

doi:10.3934/math.2023966

AIMS Mathematics

2023, Volume 8, Issue 8: 18964-18981. doi: 10.3934/math.2023966

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Research article

A survey of KdV-CDG equations via nonsingular fractional operators

1.
Department of Mathematics, University of Malakand, Chakdara, Dir Lower, Khyber Pakhtunkhwa, Pakistan
2.
Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon
3.
Near East University, Operational Research Center in Healthcare, Nicosia 99138, TRNC Mersin 10, Turkey
4.
Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, Roma 3900186, Italy
5.
Department of Mathematic, College of Science, Taif University, P. O. Box 11099, Taif 21944, Saudi Arabia

Received: 15 February 2023 Revised: 16 April 2023 Accepted: 24 April 2023 Published: 05 June 2023
MSC : 26A33, 35Q53

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.
- KdV-CDG equation,
- Laplace transform,
- Atangana-Baleanu-Caputo operator,
- fixed point theory
Citation: Ihsan Ullah, Aman Ullah, Shabir Ahmad, Hijaz Ahmad, Taher A. Nofal. A survey of KdV-CDG equations via nonsingular fractional operators[J]. AIMS Mathematics, 2023, 8(8): 18964-18981. doi: 10.3934/math.2023966

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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.

References

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