Abstract
This paper is a survey of the recent results of the author for various classes of boundary value problems for Hilfer fractional differential equations and inclusions of fractional order in (1,2] supplemented with different kinds of nonlocal boundary conditions.
Highlights
We present existence and uniqueness results for boundary value problems for Hilfer, ψ-Hilfer fractional, and sequential fractional differential equations and inclusions with a variety of nonlocal boundary conditions, such as multipoint, integral, integral multipoint, integro-multipoint, integro-multistrip-multipoint and Riemann–Stieltjes integral multistrip
A function x ∈ AC ([ a, b], R) is said to be a solution of the problem (4) if there exists a function v ∈ L1 ([ a, b], R) with v(t) ∈ F (t, x ) for a.e. t ∈ [ a, b] such that x satisfies the differential equation H D α,β x (t) = v(t) on [ a, b] and the boundary conditions x ( a) = 0, x (b) =
Our existence results for convex- and nonconvex-valued multifunctions, based, respectively, on the Leray–Schauder nonlinear alternative for multivalued maps maps and Covitz and Nadler fixed point theorem for contractive multivalued maps, are as follows
Summary
Fractional differential equations involving Hilfer derivative have many applications; see [11,12,13,14,15,16] and references cited therein This survey is devoted to articles published by the author and his collaborators and concern some recent existence and uniqueness results for various classes of boundary value problems for Hilfer fractional differential equations and inclusions of fractional order in The rest of this survey is organized as follows.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
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.