Analysis of positive fractional-order neutral time-delay systems

Huseynov I. T., Mahmudov N.

Journal of the Franklin Institute, vol.359, no.1, pp.294-330, 2022 (SCI-Expanded, Scopus) identifier

  • Nəşrin Növü: Article / Article
  • Cild: 359 Say: 1
  • Nəşr tarixi: 2022
  • Doi nömrəsi: 10.1016/j.jfranklin.2021.07.001
  • jurnalın adı: Journal of the Franklin Institute
  • Jurnalın baxıldığı indekslər: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Periodicals Index Online, Aerospace Database, Communication Abstracts, INSPEC, Metadex, MLA - Modern Language Association Database, zbMATH, Civil Engineering Abstracts
  • Səhifə sayı: pp.294-330
  • Açıq Arxiv Kolleksiyası: Məqalə
  • Adres: Yox

Qısa məlumat

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.