Journal of Integral Equations and Applications

Existence of mild solutions for fractional evolution equations

Yong Zhou, Lu Zhang, and Xiao Hui Shen

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In this paper, we study the nonlocal Cauchy problems of fractional evolution equations with Riemann-Liouville derivative by considering an integral equation which is given in terms of probability density. By using the theory of Hausdorff measure of noncompactness, we establish various existence theorems of mild solutions for the Cauchy problems in the cases $C_0$ semigroup is compact or noncompact.

Article information

J. Integral Equations Applications, Volume 25, Number 4 (2013), 557-586.

First available in Project Euclid: 31 January 2014

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Zentralblatt MATH identifier

Primary: 26A33: Fractional derivatives and integrals 34A08: Fractional differential equations 35R11: Fractional partial differential equations

Fractional evolution equations integral equations Riemann-Liouville derivative mild solutions C 0semigroup measure of noncompactness


Zhou, Yong; Zhang, Lu; Shen, Xiao Hui. Existence of mild solutions for fractional evolution equations. J. Integral Equations Applications 25 (2013), no. 4, 557--586. doi:10.1216/JIE-2013-25-4-557.

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