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Zbl 1228.65136
Lv, Zhi-Wei; Liang, Jin; Xiao, Ti-Jun
Solutions to the Cauchy problem for differential equations in Banach spaces with fractional order. (English)
[J] Comput. Math. Appl. 62, No. 3, 1303-1311 (2011). ISSN 0898-1221

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.
MSC 2000:
*65L99 Numerical methods for ODE
34K05 General theory of functional-differential equations
34A08
45K05 Integro-partial differential equations

Keywords: fractional differential equation; monotone iterative technique; cone; Banach space

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