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Some analytical properties of solutions of differential equations of noninteger order. (English) Zbl 1069.34002
Summary: Analytical properties of solutions of the nonlinear differential equation \(x^{(\alpha)}(t)= f(t,x)\), \(\alpha\in\mathbb{R}\), \(0< \alpha\leq 1\), of noninteger order are investigated. We obtain two results concerning the frame curves of solutions. Moreover, we prove a result on a differential inequality with fractional derivatives.

MSC:
34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
26A33 Fractional derivatives and integrals
26D10 Inequalities involving derivatives and differential and integral operators
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