Nonlocal Sequential Boundary Value Problems for Hilfer Type Fractional Integro-Differential Equations and Inclusions

被引：12

作者：

Phuangthong, Nawapol ^{[1
]}

Ntouyas, Sotiris K. ^{[2
,3
]}

Tariboon, Jessada ^{[1
]}

Nonlaopon, Kamsing ^{[4
]}

机构：

[1] King Mongkuts Univ Technol North Bangkok, Fac Appl Sci, Dept Math, Intelligent & Nonlinear Dynam Innovat Res Ctr, Bangkok 10800, Thailand

[2] Univ Ioannina, Dept Math, Ioannina 45110, Greece

[3] King Abdulaziz Univ, Fac Sci, Dept Math, Nonlinear Anal & Appl Math NAAM Res Grp, POB 80203, Jeddah 21589, Saudi Arabia

[4] Khon Kaen Univ, Fac Sci, Dept Math, Khon Kaen 40002, Thailand

来源：

MATHEMATICS | 2021年 / 9卷 / 06期

关键词：

fractional differential equations and inclusions; Hilfer fractional derivative; Riemann– Liouville fractional derivative; Caputo fractional derivative; boundary value problems; existence and uniqueness; fixed point theory;

D O I：

10.3390/math9060615

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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'skii, 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.

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页数：19

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