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On nonlinear coupled evolution system with nonlocal subsidiary conditions under fractal‐fractional order derivative
Author(s) -
Abdo Mohammed S.,
Abdeljawad Thabet,
Shah Kamal,
Ali Saeed M.
Publication year - 2021
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.7210
Subject(s) - mathematics , uniqueness , nonlinear system , fractional calculus , fractal , stability (learning theory) , fixed point theorem , mathematical analysis , order (exchange) , computer science , physics , finance , quantum mechanics , machine learning , economics
In the given paper, we develop and extend a qualitative analysis of a novel nonlinear system of fractional pantograph evolution differential equations (FPEDEs) involving fractal‐fractional derivative in Atangana‐Baleanu sense. To discuss the proposed problem, we establish the essential conditions for the existence and uniqueness results. The used arguments for the analysis are the fixed point techniques of Banach and Krasnoselskii. Moreover, the Ulam‐Hyers stability of solutions for the system at hand is discussed. Two interesting pertinent examples are presented.