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Existence and controllability results for stochastic impulsive integro-differential equations with infinite delay

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Abstract

In this work, the existence and the controllability of impulsive stochastic integro-differential equations with infinite delay are investigated. Unlike previous papers, the result of this one relies upon some weaker assumptions using a recently defined measure of noncompactness, resolvent operator solution in sense of Grimmer and Mönch fixed point theorem. The semigroup is only required to be strongly continuous. At the end, examples are presented to illustrate the obtained result.

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Acknowledgements

the authors would thank the anonymous referee.

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Author notes

  1. Slama Abdeldjalil and Abdelghani Ouahab contributed equally to this work.

Authors and Affiliations

  1. Laboratory of Mathematics Modeling and Applications, University of Adrar, National Road No. 06, Adrar, 01000, Algeria

    Oussama Melati & Abdeldjalil Slama

  2. Laboratory of Mathematics, University of Sidi-Bel-Abbes, Sidi Bel Abbes, 22000, Algeria

    Abdelghani Ouahab

Authors
  1. Oussama Melati
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  2. Abdeldjalil Slama
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  3. Abdelghani Ouahab
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All authors contributed to the study conception and design. All authors read and approved the final manuscript.

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Correspondence to Oussama Melati.

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Melati, O., Slama, A. & Ouahab, A. Existence and controllability results for stochastic impulsive integro-differential equations with infinite delay. Afr. Mat. 34, 24 (2023). https://doi.org/10.1007/s13370-023-01069-1

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