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Basic theory of fractional differential equations. (English) Zbl 1161.34001

This short paper addresses two interesting problems: establishing the comparison principle for fractional differential equations (FDEs), establishing the global existence theorem of FDEs. Here, the fractional derivative is in the sense of Riemann-Louville. Local existence results are also included but they are not new.

MSC:

34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
34A99 General theory for ordinary differential equations
26A33 Fractional derivatives and integrals
34C11 Growth and boundedness of solutions to ordinary differential equations
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