Analysis of positive fractional-order neutral time-delay systems. (English) Zbl 1480.93207
Summary: In this paper, we consider an initial value problem for linear matrix coefficient systems of the fractional-order neutral differential equations with two incommensurate constant delays in Caputo’s sense. Firstly, we introduce the exact analytical representation of solutions to linear homogeneous and non-homogeneous neutral fractional-order differential-difference equations system by means of newly defined delayed Mittag-Leffler type matrix functions. Secondly, a criterion on the positivity of a class of fractional-order linear homogeneous time-delay systems has been proposed. Furthermore, we prove the global existence and uniqueness of solutions to non-linear fractional neutral delay differential equations system using the contraction mapping principle in a weighted space of continuous functions with regard to classical Mittag-Leffler functions. In addition, Ulam-Hyers stability results of solutions are attained based on fixed-point approach. Finally, we present an example to demonstrate the applicability of our theoretical results.
MSC:
| 93C28 | Positive control/observation systems |
| 93C15 | Control/observation systems governed by ordinary differential equations |
| 26A33 | Fractional derivatives and integrals |
| 93D99 | Stability of control systems |
| 93C43 | Delay control/observation systems |
Keywords:
fractional-order neutral differential equations; positive fractional-order time-delay systems; Ulam-Hyers stabilityReferences:
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