Controllability of Fractional Integro-Differential Equations with Delays and Singular Kernels in Fréchet Spaces

Fatima Mesri, Abdelkrim Salim () and Mouffak Benchohra
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Fatima Mesri: Laboratory of Mathematics, Djillali Liabes University of Sidi Bel-Abbès, P.O. Box 89, Sidi Bel-Abbès 22000, Algeria
Abdelkrim Salim: Laboratory of Mathematics, Djillali Liabes University of Sidi Bel-Abbès, P.O. Box 89, Sidi Bel-Abbès 22000, Algeria
Mouffak Benchohra: Laboratory of Mathematics, Djillali Liabes University of Sidi Bel-Abbès, P.O. Box 89, Sidi Bel-Abbès 22000, Algeria

Mathematics, 2025, vol. 13, issue 22, 1-15

Abstract: This paper is devoted to the investigation of existence and approximate controllability results for a class of fractional integro-differential equations formulated in Fréchet spaces. The analysis is carried out using a generalized version of Darbo’s fixed point theorem adapted to Fréchet spaces, combined with the concept of the measure of noncompactness. To demonstrate the validity and applicability of the theoretical findings, an illustrative example is presented to demonstrate the applicability and validity of the theoretical findings.

Keywords: fractional integro-differential equations; mild solution; semigroup; Fréchet space; controllability; singular kernels (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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