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On solvability of nonlinear fractional differential systems involving nonlocal initial conditions
Author(s) -
Matar Mohammed M.,
Abu Skhail Esmail S.,
Alzabut Jehad
Publication year - 2019
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.5910
Subject(s) - mathematics , uniqueness , nonlinear system , fractional calculus , fixed point theorem , order (exchange) , mathematical analysis , banach space , banach fixed point theorem , physics , finance , quantum mechanics , economics
This paper investigates the existence and uniqueness of solutions for nonlinear fractional differential systems with order α ∈(1,2]. The system involves fractional derivative of different order in the nonlinearity and associated with nonlocal initial conditions which are defined by arbitrary operators. Our approach is based on the implementation of the Banach and Schauder fixed point theorems. Two examples are provided to examine the theoretical findings.