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Existence results for Riemann–Liouville fractional evolution inclusions in Banach spaces

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Abstract

The aim of this work is to study the existence of mild solution for semi-linear fractional evolution inclusions involving Riemann–Liouville derivative in Banach space. We prove our main result by introducing a regular measure of noncompactness in weighted space of continuous functions and using the condensing multivalued maps theory. Our result improve and complement several earlier related works. An example is given to illustrate the applications of the abstract result.

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Acknowledgements

The authors wishes to thank the referee for his (her) corrections and remarks which helped to improve the paper.

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Authors and Affiliations

  1. Département de Mathématiques, Faculté Des Sciences Semlalia, Université Cadi Ayyad, B.P. 2390, Marrakech, Morocco

    El Hadi Ait Dads

  2. UMMISCO, UMI 209, Sorbonne université, IRD, Bondy, France

    El Hadi Ait Dads

  3. Department of mathematics, École normale supérieure-Taleb Abderrahmane, B.P. 4033, 03000, Laghouat, Algeria

    Mohammed Benyoub

  4. Faculty of Mathematics and Informatics, Ibn Khaldoun University, B.P. 78, 14000, Tiaret, Algeria

    Mohamed Ziane

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  1. El Hadi Ait Dads
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  2. Mohammed Benyoub
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  3. Mohamed Ziane
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Correspondence to Mohamed Ziane.

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Dads, E.H.A., Benyoub, M. & Ziane, M. Existence results for Riemann–Liouville fractional evolution inclusions in Banach spaces. Afr. Mat. 32, 317–331 (2021). https://doi.org/10.1007/s13370-020-00828-8

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  • DOI: https://doi.org/10.1007/s13370-020-00828-8

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