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Study a class of nonlinear fractional non-autonomous evolution equations with delay

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Abstract

In this paper, we deal with a class of nonlinear fractional non-autonomous evolution equations with delay by using Hilfer fractional derivative, which generalized the famous Riemann–Liouville fractional derivative. Combining techniques of fractional calculus, measure of noncompactness and some fixed point theorem, we obtain new existence result of mild solutions when the associated semigroup is not compact. Furthermore, the assumptions that the nonlinear term satisfies some growth condition and noncompactness measure condition. The results obtained improve and extend some related conclusions. Finally, two examples will be presented to illustrate the main results.

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Acknowledgements

We wish to thank the referees for their valuable comments.

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Authors and Affiliations

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou, 730070, People’s Republic of China

    Haide Gou & Baolin Li

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  1. Haide Gou
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  2. Baolin Li
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All authors contributed equally to the writing of this paper. All authors read and approved the final manuscript.

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Correspondence to Baolin Li.

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All the authors declare that they have no competing interests.

Additional information

Supported by the National Natural Science Foundation of China (Grant No. 11061031).

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Gou, H., Li, B. Study a class of nonlinear fractional non-autonomous evolution equations with delay. J. Pseudo-Differ. Oper. Appl. 10, 155–176 (2019). https://doi.org/10.1007/s11868-017-0234-8

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  • DOI: https://doi.org/10.1007/s11868-017-0234-8

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