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Existence of mild solutions to Hilfer fractional evolution equations in Banach space

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Abstract

In this paper, we investigate the existence of mild solutions to semilinear evolution fractional differential equations with non-instantaneous impulses, using the concepts of equicontinuous \((\alpha ,\beta )\)-resolvent operator function \({\mathbb {P}}_{\alpha ,\beta }(t)\) and Kuratowski measure of non-compactness in Banach space \(\varOmega\).

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Acknowledgements

We thank Prof. Dr. E. Capelas de Oliveira for fruitful discussions for suggesting several references on the subject, and we are grateful to the anonymous referees for the suggestions that improved the manuscript. J. Vanterler acknowledges the financial support of a PNPDCAPES (process number no. 88882.305834/2018-01) scholarship of the Postgraduate Program in Applied Mathematics of IMECC-Unicamp.

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Authors and Affiliations

  1. Department of Applied Mathematics, State University of Campinas (UNICAMP)-Imecc, Campinas, SP, 13083-859, Brazil

    J. Vanterler da C. Sousa

  2. Department of Mathematics, Çankaya University, 06790, Ankara, Turkey

    Fahd Jarad

  3. Department of Mathematics and Physical Sciences, Prince Sultan University, P. O. Box 66833, Riyadh, 11586, Saudi Arabia

    Thabet Abdeljawad

  4. Department of Medical Research, China Medical University, 40402, Taichung, Taiwan

    Thabet Abdeljawad

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  1. J. Vanterler da C. Sousa
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  2. Fahd Jarad
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  3. Thabet Abdeljawad
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Correspondence to J. Vanterler da C. Sousa.

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Communicated by Feng Dai.

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Sousa, J.V.d.C., Jarad, F. & Abdeljawad, T. Existence of mild solutions to Hilfer fractional evolution equations in Banach space. Ann. Funct. Anal. 12, 12 (2021). https://doi.org/10.1007/s43034-020-00095-5

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  • DOI: https://doi.org/10.1007/s43034-020-00095-5

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