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Analysis of Abstract Partial Impulsive Integro-Differential System with Delay via Integrated Resolvent Operator

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Abstract

In this manuscript, we employ integrated resolvent operator to derive the variation of constants formula for the solution of the impulsive integro-differential system, in nonlocal domain with finite delay function. Using the Banach fixed point theorem and integrated resolvent operator, we explore the existence of mild solution of the aforementioned system. Additionally, we establish the Hyers–Ulam stability of the system. Finally, the main result is illustrated with the help of an example.

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  1. Department of Mathematics, University of Peshawar, Peshawar, 25000, Pakistan

    Ishfaq Khan & Akbar Zada

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  1. Ishfaq Khan
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  2. Akbar Zada
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Khan, I., Zada, A. Analysis of Abstract Partial Impulsive Integro-Differential System with Delay via Integrated Resolvent Operator. Qual. Theory Dyn. Syst. 23, 110 (2024). https://doi.org/10.1007/s12346-024-00968-3

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