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Regularity of mild Solutions for fractional abstract Cauchy problem with order \({\alpha \in (1, 2)}\)

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Abstract

In this paper, we deal with the regularity of mild Solutions for fractional abstract Cauchy problem with order \({\alpha \in (1, 2)}\). Based on properties of solution operator and analytic solution operator, we obtain the sufficient condition under which a mild solution becomes a classical solution, and if the Cauchy problem has an analytic solution operator, we obtain more stronger results.

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Authors and Affiliations

  1. College of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing, Jiangsu, 210044, People’s Republic of China

    Yaning Li

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  1. Yaning Li
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Correspondence to Yaning Li.

Additional information

The research was supported by the Startup Foundation for Introducing Talent of NUIST (S8113097001), the National Natural Science Foundation of China (Grant no. 71501101), and the Natural Science Foundation of Jiangsu Province (Grant no. SBK2015041898).

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Li, Y. Regularity of mild Solutions for fractional abstract Cauchy problem with order \({\alpha \in (1, 2)}\) . Z. Angew. Math. Phys. 66, 3283–3298 (2015). https://doi.org/10.1007/s00033-015-0577-z

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  • DOI: https://doi.org/10.1007/s00033-015-0577-z

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