Multi-Point Boundary Value Problems for (k, ϕ)-Hilfer Fractional Differential Equations and Inclusions

Axioms

卷:11

Ayub Samadi¹  Sotiris K. Ntouyas²  Jessada Tariboon³ 

[1] Department of Mathematics, Miyaneh Branch, Islamic Azad University, Miyaneh, Iran;

[2] Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece;

[3] Intelligent and Nonlinear Dynamic Innovations, Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand;

关键词: (k, ϕ)-Hilfer fractional derivative;    Riemann-Liouville fractional derivative;    Caputo fractional derivative;    existence;    uniqueness;    fixed point theorems;   

DOI  :  10.3390/axioms11030110

来源: DOAJ

【 摘 要 】

In this paper we initiate the study of boundary value problems for fractional differential equations and inclusions involving $(k,\varphi )$-Hilfer fractional derivative of order in $(1,2]$. In the single-valued case the existence and uniqueness results are established by using classical fixed-point theorems, such as Banach, Krasnoselskiĭ and Leray-Schauder. In the multivalued case we consider both cases, when the right-hand side has convex or non-convex values. In the first case, we apply the Leray–Schauder nonlinear alternative for multivalued maps, and in the second, the Covit–Nadler fixed-point theorem for multivalued contractions. All results are well illustrated by numerical examples.

【 授权许可】

Unknown