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

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  • Valentin Keyantuo
  • Carlos Lizama
  • Mahamadi Warma

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,

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Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:614328
DOI: 10.1155/2013/614328
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