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

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-ord...

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Bibliographic Details
Published inAIMS mathematics Vol. 8; no. 7; pp. 15773 - 15788
Main Authors Boutiara, Abdelatif, Rhaima, Mohamed, Mchiri, Lassaad, Makhlouf, Abdellatif Ben
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2023
Subjects
fractional $ {(p
global convergence
measure of non-compactness
meir-keeler condensing operators
q)} $-calculus
successive approximations
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Summary: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.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2023805