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, issue 1

Abstract: We investigate mild solutions of the fractional order nonhomogeneous Cauchy problem Dtαu(t)=Au(t)+f(t), t>0, where 0 0 in which Φα is a Wright type function. For the first order case, that is, α = 1, the corresponding result was proved by Prüss in 1984. In case X is a Banach lattice and the semigroup (T(t)) t≥0 is positive, we obtain existence of solutions of the semilinear problem Dtαu(t)=Au(t)+f(t,u(t)), t>001,

Date: 2013
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https://doi.org/10.1155/2013/614328

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:614328

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