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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