Stability regions for linear fractional differential systems and their discretizations

Stability regions for fractional differential systems with a time delay

“…[9]). Finally, (2.1) may serve as the test system either for numerical analysis of FDDEs (for a similar situation in the fractional non-delayed case we refer to [22,23]), or for stability investigations of FDDEs via other methods (for basic principles of Lyapunov methods for FDDEs see, e.g. [24]).…”

Weighted bounded solutions for a class of nonlinear fractional equations.

“…l p spaces. We notice that, recently, this approach by means of the z-transform has been followed by other authors, see [11,12]. It is also interesting to note that it was recently proved that different notions of fractional sum, existing in the current literature, are equivalent with Definition 2.1 modulo translation, see [10].…”

Asymptotic Stability Of Dynamic Equations With Two Fractional Terms: Continuous Versus Discrete Case

“…It can be illustrated by the discrete analogue of the Matignon criterion which shows that discrete stability areas for linear autonomous fractional systems have a difficult structure compared to the stability sectors described in the Matignon criterion (see [13] versus [5]). For some other introductory papers on stability of linear fractional difference equations we refer to [1], [3] and [4].…”