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Local and global existence theorems on differential equations of non-integer order. (English) Zbl 0839.34003

Summary: Local and global existence and uniqueness theorems of the nonlinear differential equation \(x^{(\alpha)} (t) = f(t,x)\), \(\alpha \in \mathbb{R}\), \(0 < \alpha \leq 1\), of nonintegral order are obtained. Our method is an application of fixed-point theorems.

MSC:

34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
26A33 Fractional derivatives and integrals
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