Controllability of Fractional Integro-Differential Equations with Infinite Delay and Singular Kernels in Banach Spaces
Fatima Mesri1, Abdelkrim Salim2, Khalida Aissani1 and Mouffak Benchohra1
1Laboratory of Mathematics, Djillali Liabes University of Sidi Bel-Abbes, P.O. Box 89, Sidi Bel-Abbes 22000, Algeria
2Faculty of Technology, Hassiba Benbouali University of Chlef, P.O. Box 151 Chlef 02000, Algeria
Received on May 3, 2026
Accepted on May 22, 2026
Communicated by Gaston M. N'Guérékata
| Abstract. In this paper, we investigate the existence and controllability of a class of fractional integro-differential equations with infinite delay and a weakly singular kernel in the setting of Banach spaces. The analysis is primarily developed through the framework of semigroup theory, in conjunction with Mönch’s fixed point theorem and the properties of measures of noncompactness. To validate the theoretical findings, a carefully constructed example is provided, demonstrating the applicability and effectiveness of the proposed approach. | |
| Keywords: | Functional integro-differential equations; mild solution; semigroup; Banach space; controllability; singular kernels. |
| 2010 Mathematics Subject Classification: 47H08, 34K30, 93C20, 45J05. | |
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