Abstract and Applied Analysis

Positive Solutions for the Initial Value Problem of Fractional Evolution Equations

He Yang and Yue Liang

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By using the fixed point theorems and the theory of analytic semigroup, we investigate the existence of positive mild solutions to the Cauchy problem of Caputo fractional evolution equations in Banach spaces. Some existence theorems are obtained under the case that the analytic semigroup is compact and noncompact, respectively. As an example, we study the partial differential equation of the parabolic type of fractional order.

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Abstr. Appl. Anal., Volume 2013 (2013), Article ID 428793, 7 pages.

First available in Project Euclid: 27 February 2014

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Yang, He; Liang, Yue. Positive Solutions for the Initial Value Problem of Fractional Evolution Equations. Abstr. Appl. Anal. 2013 (2013), Article ID 428793, 7 pages. doi:10.1155/2013/428793. https://projecteuclid.org/euclid.aaa/1393511818

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