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Ponce, Rodrigo

Existence of mild solutions to nonlocal fractional Cauchy problems via compactness. (English) Zbl 1470.34025

Abstr. Appl. Anal. 2016, Article ID 4567092, 15 p. (2016).
Summary: We obtain characterizations of compactness for resolvent families of operators and as applications we study the existence of mild solutions to nonlocal Cauchy problems for fractional derivatives in Banach spaces. We discuss here simultaneously the Caputo and Riemann-Liouville fractional derivatives in the cases \(0 < \alpha < 1\) and \(1 < \alpha < 2 \).

Cited in 11 Documents

MSC:

34A08 Fractional ordinary differential equations
34G20 Nonlinear differential equations in abstract spaces
47D03 Groups and semigroups of linear operators
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\textit{R. Ponce}, Abstr. Appl. Anal. 2016, Article ID 4567092, 15 p. (2016; Zbl 1470.34025)
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References:

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