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Fractional differential equations of Sobolev type with sectorial operators

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Abstract

This paper treats the asymptotic behavior of resolvent operators of Sobolev type and its applications to the existence and uniqueness of mild solutions to fractional functional evolution equations of Sobolev type in Banach spaces. We first study the asymptotic decay of some resolvent operators (also called solution operators) and next, by using fixed point results, we obtain the existence and uniqueness of solutions to a class of Sobolev type fractional differential equation. We notice that, the existence or compactness of an operator \(E^{-1}\) is not necessarily needed in our results.

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Acknowledgements

The authors are grateful to the editor and anonymous referees for carefully reading this manuscript and giving valuable suggestion for improvements. Part of this work was done while S. Rueda was in the Master degree program in Mathematics at the Universidad de Talca.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Xidian University, Xi’an, 710071, Shaanxi, China

    Yong-Kui Chang

  2. Instituto de Matemática y Física, Universidad de Talca, Casilla 747, Talca, Chile

    Rodrigo Ponce

  3. Departamento de Matemática y Computación, Universidad de Santiago de Chile, Casilla 307-Correo 2, Santiago, Chile

    Silvia Rueda

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  1. Yong-Kui Chang
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  2. Rodrigo Ponce
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  3. Silvia Rueda
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Correspondence to Rodrigo Ponce.

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Communicated by Abdelaziz Rhandi.

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Yong-Kui Chang was partially supported by NSFRP of Shaanxi Province (2017JM1017), Rodrigo Ponce was partially supported by FONDECYT Grant #11130619 and the work of Silvia Rueda was funded by the CONICYT-PFCHA/Doctorado Nacional/2017-21171405.

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Chang, YK., Ponce, R. & Rueda, S. Fractional differential equations of Sobolev type with sectorial operators. Semigroup Forum 99, 591–606 (2019). https://doi.org/10.1007/s00233-019-10038-9

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