@article{Boutiara2023, 
author = {Abdelatif Boutiara and Mohamed Rhaima and Lassaad Mchiri and Abdellatif Ben Makhlouf},
title = {Cauchy problem for fractional        (    p    ,    q    )  -difference equations},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {7},
pages = {15773-15788},
keywords = {fractional (p, q)-calculus, global convergence, successive approximations, measure of non-compactness, Meir-Keeler condensing operators},
url = {https://www.sciopen.com/article/10.3934/math.2023805},
doi = {10.3934/math.2023805},
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.}
}