Existence of solutions for the delayed nonlinear fractional functional differential equations with three-point integral boundary value conditions

This paper is concerned with the three-point integral boundary value problems of time-delay nonlinear fractional functional differential equations involving Caputo fractional derivatives of order alpha is an element of (2, 3). By employing the Schauder fixed point theorem, the Banach contraction principle, and a nonlinear alternative of Leray-Schauder type, some sufficient criteria are established to guarantee the existence of solutions. Our study improves and extends the previous results in the literature. As applications, some examples are provided to illustrate our main results.