Abstract
Abstract In this paper, we study three-point boundary value problems of the following fractional functional differential equations involving the Caputo fractional derivative: "Equation missing" where D α C , D β C denote Caputo fractional derivatives, 2 < α < 3 , 0 < β < 1 , η ∈ ( 0 , 1 ) , 1 < λ < 1 2 η . 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.
Highlights
Fractional calculus is a branch of mathematics, it is an emerging field in the area of the applied mathematics that deals with derivatives and integrals of arbitrary orders as well as with their applications
We study three-point boundary value problems of the following fractional functional differential equations involving the Caputo fractional derivative: CDαu(t) = f (t, ut, CDβ u(t)), 0 < t < 1, u (0) = 0, u (1) = λu (η), where CDα, CDβ denote Caputo fractional derivatives, 2 < α < 3, 0 < β < 1, η ∈ (0, 1)
There have been many papers focused on boundary value problems of fractional ordinary differential equations [ – ] and an initial value problem of fractional functional differential equations [ – ]
Summary
Green function to reformulate boundary value problems into an abstract operator equation.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
