Existence of Mild Solution of the Hilfer Fractional Differential Equations with Infinite Delay on an Infinite Interval

被引：4

作者：

Bose, Chandrabose Sindhu Varun ^{[1
]}

Udhayakumar, Ramalingam ^{[1
]}

Savatovic, Milica ^{[2
]}

Deiveegan, Arumugam ^{[3
]}

Todorcevic, Vesna ^{[4
]}

Radenovic, Stojan ^{[5
]}

机构：

[1] Vellore Inst Technol, Sch Adv Sci, Dept Math, Vellore 632014, Tamil Nadu, India

[2] Univ Belgrade, Sch Elect Engn, Bulevar Kralja Aleksandra 73, Belgrade 11000, Serbia

[3] Sona Coll Technol, Dept Math, Salem 636005, Tamilnadu, India

[4] Univ Belgrade, Serbian Acad Sci & Arts, Fac Org Sci, Dept Math,Math Inst, Jove Il 154, Belgrade 11000, Serbia

[5] Univ Belgrade, Fac Mech Engn, Belgrade 11000, Serbia

来源：

FRACTAL AND FRACTIONAL | 2023年 / 7卷 / 10期

关键词：

Hilfer fractional derivative; mild solution; fixed-point theorem; infinite interval; CONTROLLABILITY; SYSTEMS;

D O I：

10.3390/fractalfract7100724

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this study, we present a mild solution to the Hilfer fractional differential equations with infinite delay. Firstly, we establish the results on an infinite interval; to achieve this, we use the generalized Ascoli-Arzela theorem and Monch's fixed point theorem via a measure of noncompactness. Secondly, we consider the existence of a mild solution when the semigroup is compact, and the Schauder fixed-point theorem is used. The outcome is demonstrated using an infinitesimal operator, fractional calculus, semigroup theory, and abstract space. Finally, we present an example to support the results.

引用

页数：12

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