On the discrete delayed perturbation of Mittag-Leffler functions and their application to Caputo-type fractional difference equations

Aydın M., Mahmudov N.

Journal of Analysis, vol.33, no.5, pp.2521-2545, 2025 (ESCI, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 33 Issue: 5
  • Publication Date: 2025
  • Doi Number: 10.1007/s41478-025-00954-1
  • Journal Name: Journal of Analysis
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus
  • Page Numbers: pp.2521-2545
  • Keywords: Discrete delayed perturbation, Fractional difference, Linear system, Nabla Mittag-Leffler, Time-delay
  • Open Archive Collection: Article
  • Azerbaijan State University of Economics (UNEC) Affiliated: Yes

Abstract

The linear nonhomogeneous Caputo-type fractional difference system with constant coefficients is introduced. An explicit solution to the system is acquired by proposing a newly discrete retarded perturbation of the nabla Mittag-Leffer-type function containing such matrix equations that provide non-permutability. A couple of special cases obtained from our results are discussed.