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Existence of Integro-Differential Neutral Measure Driven System Using Monotone Iterative Technique and Measure of Noncompactness

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Abstract

In present manuscript, we bring into work the technique of lower and upper solutions incorporated with the monotone iterative technique to discuss the existence and uniqueness of extremal mild solutions for integro-differential neutral measure driven system in an ordered Banach space. A strenuous situation of Zeno behaviour arising in enormous hybrid systems can also be modeled under our general system. Measure driven system is also a more generalized concept as compared to ordinary differential equation. We established the results in space of regulated functions. Our main findings are obtained by using the monotone iterative technique, theory of Bochner–Stieltjes integral, measure of noncompactness, regulated functions and semigroup theory. In the end, we provide an application to justify our results.

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Acknowledgements

The first author is supported by the Council of Scientific & Industrial Research (CSIR), India (Award No.: 09/045(1551)/2017-EMR-I).

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  1. Department of Mathematics, Akal University, Talwandi Sabo, Bathinda, Punjab, 151302, India

    Syed Mohammad Abdal

  2. Department of Mathematics, University of Delhi, Delhi, India

    Surendra Kumar

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  1. Syed Mohammad Abdal
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  2. Surendra Kumar
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Correspondence to Syed Mohammad Abdal.

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Abdal, S.M., Kumar, S. Existence of Integro-Differential Neutral Measure Driven System Using Monotone Iterative Technique and Measure of Noncompactness. Differ Equ Dyn Syst (2022). https://doi.org/10.1007/s12591-022-00614-x

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