Some analytical properties of solutions of differential equations of noninteger order. (English) Zbl 1069.34002

Momani, S. M.; Hadid, S. B.; Alawenh, Z. M.

Int. J. Math. Math. Sci. 2004, No. 13-16, 697-701 (2004).

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