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

Lakshmikantham, V.; Vatsala, A. S.

Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 69, No. 8, 2677-2682 (2008).

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.

Reviewer: Li Changpin (Logan)

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

Keywords:

fractional differential equations; basic theory of existence; comparison result

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