Existence and controllability of integrodifferential equations with non-instantaneous impulses in Fréchet spaces

Abdelhamid Bensalem; Abdelkrim Salim; Bashir Ahmad; Mouffak Benchohra

doi:10.56754/0719-0646.2502.231

DOI:

https://doi.org/10.56754/0719-0646.2502.231

Abstract

In this paper, we investigate existence of mild solutions to a non-instantaneous integrodifferential equation via resolvent operators in the sense of Grimmer in Fréchet spaces. Utilizing the technique of measures of noncompactness in conjunction with the Darbo's fixed point theorem, we present sufficient criteria ensuring the controllability of the given problem. An illustrative example is also discussed.

Keywords

Integrodifferential equation , mild solution , measures of noncompactness , resolvent operator controllability , fixed point theorem , Fréchet space

Mathematics Subject Classification:

93B05 , 34D23 , 47H10 , 46A04 , 45J05 , 47H08 , 35D30 , 47B40

Abdelhamid Bensalem Laboratory of Mathematics, Djillali Liabes University of Sidi Bel-Abbès, P.O. Box 89, Sidi Bel-Abbès 22000, Algeria. https://orcid.org/0009-0008-9169-148X
Abdelkrim Salim Laboratory of Mathematics, Djillali Liabes University of Sidi Bel-Abbès, P.O. Box 89, Sidi Bel-Abbès 22000, Algeria – Faculty of Technology, Hassiba Benbouali University of Chlef, P.O. Box 151 Chlef 02000, Algeria. https://orcid.org/0000-0003-2795-6224
Bashir Ahmad Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia. https://orcid.org/0000-0001-5350-2977
Mouffak Benchohra Laboratory of Mathematics, Djillali Liabes University of Sidi Bel-Abbès, P.O. Box 89, Sidi Bel-Abbès 22000, Algeria – Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia. https://orcid.org/0000-0003-3063-9449

Pages: 231–250
Date Published: 2023-08-05
Vol. 25 No. 2 (2023)

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