Abstract
In the present research, we study boundary value problems for fractional integro-differential equations and inclusions involving the Hilfer fractional derivative. Existence and uniqueness results are obtained by using the classical fixed point theorems of Banach, Krasnosel’skiĭ, and Leray–Schauder in the single-valued case, while Martelli’s fixed point theorem, a nonlinear alternative for multivalued maps, and the Covitz–Nadler fixed point theorem are used in the inclusion case. Examples are presented to illustrate our results.
Highlights
In last few decades, fractional differential equations with initial/boundary conditions have been studied by many researchers
Motivated by the research going in this direction, in the present paper, we study existence and uniqueness of solutions for the following new class of boundary value problems consisting of fractional-order sequential Hilfer-type differential equations supplemented with nonlocal integro-multipoint boundary conditions of the form
For possible nonconvex-valued maps, we obtain an existence result by using Covitz–Nadler fixed point theorem [20] for contractive maps
Summary
Fractional differential equations with initial/boundary conditions have been studied by many researchers. Several authors have studied initial value problems involving Hilfer fractional derivatives, see, for example, [12,13,14] and the references included therein. Boundary value problems for the Hilfer fractional derivative and nonlocal boundary conditions were initiated in [15]. Consisting of fractional-order sequential Hilfer-type differential equations supplemented with nonlocal integro-multipoint boundary conditions of the form. We look at the corresponding multivalued problem by studying existence of solutions for a new class of sequential boundary value problems of Hilfer-type fractional differential inclusions with nonlocal integro-multipoint boundary conditions of the form. Existence results for the sequential boundary value Problems (3) and (4) with convexvalued maps are derived by applying a fixed point theorem according to Martelli’s [19].
Sign-in/Register to view highlights & summary 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.
