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On the Cauchy Problems of Fractional Evolution Equations with Nonlocal Initial Conditions

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Abstract

In this paper, new criterions which allow us to relax the compactness and Lipschitz continuity on nonlocal item, ensuring the existence and uniqueness of mild solutions for the Cauchy problems of fractional evolution equations with nonlocal initial conditions, are established. The results obtained in this paper essentially extend some existing results in this area. Finally, we present two applications to the abstract results.

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Authors and Affiliations

  1. Department of Mathematics, Nanchang University, Nanchang, 330031, Jiangxi, People’s Republic of China

    Rong-Nian Wang & Yan-Hong Yang

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  1. Rong-Nian Wang
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  2. Yan-Hong Yang
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Correspondence to Rong-Nian Wang.

Additional information

Work supported in part by the NSF of Jiangxi Province of China (2009GQS0018) and the Youth Foundation of Jiangxi Provincial Education Department of China (GJJ10051).

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Wang, RN., Yang, YH. On the Cauchy Problems of Fractional Evolution Equations with Nonlocal Initial Conditions. Results. Math. 63, 15–30 (2013). https://doi.org/10.1007/s00025-011-0142-9

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  • DOI: https://doi.org/10.1007/s00025-011-0142-9

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