Abstract
This paper investigates the existence of solutions for higher order fractional differential inclusions with fractional integral boundary conditions involving nonintersecting finite many strips of arbitrary length. Our study includes the cases when the right-hand side of the inclusion has convex as well non-convex values. Some standard fixed point theorems for multivalued maps are applied to establish the main results. An illustrative example is also presented.
Highlights
We study a boundary value problem of a fractional differential inclusion with multi-strip fractional integral boundary conditions given by cDqx(t) ∈ F (t, x(t)), t ∈ [0, T ]
We have introduced Riemann-Liouville type fractional integral boundary conditions involving nonintersecting finite many strips of arbitrary length
We assume that F is a compact and convex valued multivalued map
Summary
We study a boundary value problem of a fractional differential inclusion with multi-strip fractional integral boundary conditions given by cDqx(t) ∈ F (t, x(t)), t ∈ [0, T ], m x(0) = 0, x′(0) = 0, . We have introduced Riemann-Liouville type fractional integral boundary conditions involving nonintersecting finite many strips of arbitrary length. The first result relies on the nonlinear alternative of Leray-Schauder type. We shall combine the nonlinear alternative of Leray-Schauder type for single-valued maps with a selection theorem due to Bressan and Colombo for lower semicontinuous multivalued maps with nonempty closed and decomposable values, while in the third result, we shall use the fixed point theorem for contraction multivalued maps due to Covitz and Nadler.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
More From: Electronic Journal of Qualitative Theory of Differential Equations
Disclaimer: 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.