Three-point boundary value problems of fractional functional differential equations with delay: Doc 292

In this paper, we study three-point boundary value problems of the following fractional functional differential equations involving the Caputo fractional derivative: [Equation not available: see fulltext.] where [InlineEquation not available: see fulltext.], [InlineEquation not available: see fulltext.] denote Caputo fractional derivatives, [InlineEquation not available: see fulltext.], [InlineEquation not available: see fulltext.], [InlineEquation not available: see fulltext.], [InlineEquation not available: see fulltext.]. We use the Green function to reformulate boundary value problems into an abstract operator equation. By means of the Schauder fixed point theorem and the Banach contraction principle, some existence results of solutions are obtained, respectively. As an application, some examples are presented to illustrate the main results. MSC: 34A08, 34K37.[PUBLICATION ABSTRACT]