Spectral Criteria for Solvability of Boundary Value Problems and Positivity of Solutions of Time-Fractional Differential Equations

Valentin Keyantuo, Carlos Lizama and Mahamadi Warma

Abstract and Applied Analysis, 2013, vol. 2013, 1-11

Abstract:

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

Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:614328

DOI: 10.1155/2013/614328

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