Authors: Varun Bose, Chandrabose Sindhu
Udhayakumar, Ramalingam
Savatović, Milica
Deiveegan, Arumugam
Todorčević, Vesna 
Radenović, Stojan
Affiliations: Mathematics 
Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Existence of Mild Solution of the Hilfer Fractional Differential Equations with Infinite Delay on an Infinite Interval
Journal: Fractal and Fractional
Volume: 7
Issue: 10
First page: 724
Issue Date: 2023
Rank: ~M21a
ISSN: 2504-3110
DOI: 10.3390/fractalfract7100724
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.
Keywords: fixed-point theorem | Hilfer fractional derivative | infinite interval | mild solution
Publisher: MDPI

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