On solvability of nonlinear fractional differential systems involving nonlocal initial conditions

摘要

This paper investigates the existence and uniqueness of solutions for nonlinear fractional differential systems with order alpha is an element of(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.