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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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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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.
AbstractList 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.
Author Mchiri, Lassaad
Boutiara, Abdelatif
Rhaima, Mohamed
Makhlouf, Abdellatif Ben
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StartPage 15773
SubjectTerms fractional $ {(p
global convergence
measure of non-compactness
meir-keeler condensing operators
q)} $-calculus
successive approximations
Title Cauchy problem for fractional $ {(p, q)} $-difference equations
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Volume 8
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