Cauchy problem for fractional $ {(p, q)} $-difference equations

Abdelatif Boutiara; Mohamed Rhaima; Lassaad Mchiri; Abdellatif Ben Makhlouf; Abdelatif Boutiara; Mohamed Rhaima; Lassaad Mchiri; Abdellatif Ben Makhlouf

doi:10.3934/math.2023805

AIMS Mathematics

2023, Volume 8, Issue 7: 15773-15788. doi: 10.3934/math.2023805

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Cauchy problem for fractional $ {(p, q)} $-difference equations

1.
Department of Mathematics and Computer Science, University of Ghardaia, BP 455 Ghardaia 47000, Algeria
2.
Department of Statistics and Operations Research, College of Sciences, King Saud University, Riyadh 11451, Saudi Arabia
3.
ENSIIE, University of Evry-Val-d'Essonne, 1 square de la Résistance 91025 Évry-Courcouronnes cedex, France
4.
Department of Mathematics, Faculty of Sciences of Sfax, University of Sfax, Tunisia

Received: 03 February 2023 Revised: 31 March 2023 Accepted: 10 April 2023 Published: 28 April 2023
MSC : 34A08

In this research article, we deal with the global convergence of successive approximations (s.a) as well as the existence of solutions to a fractional $ {(p, q)} $-difference equation. Then, we discuss the existence result of the solutions of Caputo-type $ {(p, q)} $-difference fractional vector-order equations in a Banach space. Also, we prove a theorem on the global convergence of successive approximations to the unique solution of our problem. Finally, the application of the main results is demonstrated by presenting numerical examples.
- fractional $ {(p, q)} $-calculus,
- global convergence,
- successive approximations,
- measure of non-compactness,
- Meir-Keeler condensing operators
Citation: Abdelatif Boutiara, Mohamed Rhaima, Lassaad Mchiri, Abdellatif Ben Makhlouf. Cauchy problem for fractional $ {(p, q)} $-difference equations[J]. AIMS Mathematics, 2023, 8(7): 15773-15788. doi: 10.3934/math.2023805

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Abstract

In this research article, we deal with the global convergence of successive approximations (s.a) as well as the existence of solutions to a fractional $ {(p, q)} $-difference equation. Then, we discuss the existence result of the solutions of Caputo-type $ {(p, q)} $-difference fractional vector-order equations in a Banach space. Also, we prove a theorem on the global convergence of successive approximations to the unique solution of our problem. Finally, the application of the main results is demonstrated by presenting numerical examples.

References

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