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Solutions to the Cauchy problem for differential equations in Banach spaces with fractional order. (English) Zbl 1228.65136
Summary: We use the monotone iterative technique combined with cone theory to investigate the existence of solutions to the Cauchy problem for Caputo fractional differential equations in Banach spaces. New existence theorems are obtained for the case of a cone $P$ being normal and fully regular respectively. Moreover, two examples are given to illustrate the abstract results.

65L99Numerical methods for ODE
34K05General theory of functional-differential equations
34A08Fractional differential equations
45K05Integro-partial differential equations
Full Text: DOI
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