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Positive solutions for the initial value problem of fractional evolution equations. (English) Zbl 1291.35430
Summary: By using the fixed point theorems and the theory of analytic semigroup, we investigate the existence of positive mild solutions to the Cauchy problem of Caputo fractional evolution equations in Banach spaces. Some existence theorems are obtained under the case that the analytic semigroup is compact and noncompact, respectively. As an example, we study the partial differential equation of the parabolic type of fractional order.

MSC:
35R11 Fractional partial differential equations
34A08 Fractional ordinary differential equations
34G20 Nonlinear differential equations in abstract spaces
35B09 Positive solutions to PDEs
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