Abstract:

Using Banach contraction mapping principle, the authors investigated a fractional differential system with fractional integral conditions, which involved the Caputo fractional derivative with nonlinear terms, and established Green’s function of an equivalent integral equation to the system and sufficient conditions for the existence and uniqueness of solution of the system. An example was given to illustrate the application of the result.

Key words: integral boundary value problem, fractional differential equation, Caputo fractional derivative, Banach contraction mapping principle