Abstract and Applied Analysis
- Abstr. Appl. Anal.
- Volume 2014 (2014), Article ID 430418, 9 pages.
Integrated Fractional Resolvent Operator Function and Fractional Abstract Cauchy Problem
We firstly prove that -times integrated -resolvent operator function (-ROF) satisfies a functional equation which extends that of -times integrated semigroup and -resolvent operator function. Secondly, for the inhomogeneous -Cauchy problem , , , if is the generator of an -ROF, we give the relation between the function and mild solution and classical solution of it. Finally, for the problem , , , where is a linear closed operator. We show that generates an exponentially bounded -ROF on a Banach space if and only if the problem has a unique exponentially bounded classical solution and Our results extend and generalize some related results in the literature.
Abstr. Appl. Anal., Volume 2014 (2014), Article ID 430418, 9 pages.
First available in Project Euclid: 26 March 2014
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Li, Ya-Ning; Sun, Hong-Rui. Integrated Fractional Resolvent Operator Function and Fractional Abstract Cauchy Problem. Abstr. Appl. Anal. 2014 (2014), Article ID 430418, 9 pages. doi:10.1155/2014/430418. https://projecteuclid.org/euclid.aaa/1395858516