On (k , ψ)-Hilfer Fractional Differential Equations and Inclusions with Mixed (k , ψ)-Derivative and Integral Boundary Conditions.

Autor:	Ntouyas, Sotiris K., Ahmad, Bashir, Nuchpong, Cholticha, Tariboon, Jessada
Předmět:	DIFFERENTIAL inclusions FRACTIONAL differential equations BOUNDARY value problems FRACTIONAL integrals SET-valued maps INTEGRAL operators INTEGRALS
Zdroj:	Axioms (2075-1680); Aug2022, Vol. 11 Issue 8, pN.PAG-N.PAG, 17p
Abstrakt:	In this paper we study single-valued and multi-valued (k,ψ)-Hilfer-type boundary value problems of fractional order in (1,2], subject to nonlocal boundary conditions involving (k,ψ)-Hilfer-type derivative and integral operators. The results for single-valued case are established by using Banach and Krasnosel'skiĭ fixed point theorems as well as Leray–Schauder nonlinear alternative. In the multi-valued case, we establish an existence result for the convex valued right-hand side of the inclusion via Leray–Schauder nonlinear alternative for multi-valued maps, while the second one when the right-hand side has non-convex values is obtained by applying Covitz–Nadler fixed point theorem for multi-valued contractions. Numerical examples illustrating the obtained theoretical results are also presented. [ABSTRACT FROM AUTHOR]
Databáze:	Complementary Index
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