Abstract and Applied Analysis
- Abstr. Appl. Anal.
- Volume 2013 (2013), Article ID 614328, 11 pages.
Spectral Criteria for Solvability of Boundary Value Problems and Positivity of Solutions of Time-Fractional Differential Equations
We investigate mild solutions of the fractional order nonhomogeneous Cauchy problem , where When is the generator of a -semigroup on a Banach space , we obtain an explicit representation of mild solutions of the above problem in terms of the semigroup. We then prove that this problem under the boundary condition admits a unique mild solution for each if and only if the operator is invertible. Here, we use the representation in which is a Wright type function. For the first order case, that is, , the corresponding result was proved by Prüss in 1984. In case is a Banach lattice and the semigroup is positive, we obtain existence of solutions of the semilinear problem
Abstr. Appl. Anal., Volume 2013 (2013), Article ID 614328, 11 pages.
First available in Project Euclid: 27 February 2014
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Keyantuo, Valentin; Lizama, Carlos; Warma, Mahamadi. Spectral Criteria for Solvability of Boundary Value Problems and Positivity of Solutions of Time-Fractional Differential Equations. Abstr. Appl. Anal. 2013 (2013), Article ID 614328, 11 pages. doi:10.1155/2013/614328. https://projecteuclid.org/euclid.aaa/1393512131