Existence of Mild Solution of the Hilfer Fractional Differential Equations with Infinite Delay on an Infinite Interval-Reference-Cited by-同舟云学术

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

Published:2023-09-30 Issue:10 Volume:7 Page:724
ISSN:2504-3110
Container-title:Fractal and Fractional
language:en
Short-container-title:Fractal Fract

Author:

Varun Bose Chandrabose Sindhu¹^ORCID,Udhayakumar Ramalingam¹^ORCID,Savatović Milica²,Deiveegan Arumugam³^ORCID,Todorčević Vesna⁴,Radenović Stojan⁵

Affiliation:

1. Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore 632014, Tamil Nadu, India

2. School of Electrical Engineering, University of Belgrade, Bulevar Kralja Aleksandra 73, 11000 Belgrade, Serbia

3. Department of Mathematics, Sona College of Technology, Salem 636005, Tamilnadu, India

4. Mathematical Institute of the Serbian Academy of Sciences and Arts, Department of Mathematics, Faculty of Organizational Sciences, University of Belgrade, Jove Ilica 154, 11000 Belgrade, Serbia

5. Faculty of Mechanical Engineering, University of Belgrade, 11000 Belgrade, Serbia

Abstract

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–Arzelà theorem and Mönch’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.

Publisher

MDPI AG

Subject

Statistics and Probability,Statistical and Nonlinear Physics,Analysis

Link

https://www.mdpi.com/2504-3110/7/10/724/pdf

Reference20 articles.

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4. Zhou, Y. (2014). Basic Theory of Fractional Differential Equations, World Scientific.

5. Zhou, Y. (2015). Fractional Evolution Equations and Inclusions: Analysis and Control, Elsevier.

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