General Delayed Perturbation of the Three-Parameter Mittag-Leffler Functions

Aydın M.

Mathematical Methods in the Applied Sciences, 2026 (SCI-Expanded, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Basım Tarihi: 2026
  • Doi Numarası: 10.1002/mma.70499
  • Dergi Adı: Mathematical Methods in the Applied Sciences
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Compendex, INSPEC, MathSciNet, zbMATH
  • Anahtar Kelimeler: fractional linear equation, general delay perturbation, Mittag-Leffler function, Prabhakar fractional derivative, representation of solutions
  • Van Yüzüncü Yıl Üniversitesi Adresli: Evet

Özet

In this paper, we define a general delayed perturbation of the three-parameter Mittag-Leffler type matrix function, which can be seen as a generalization of both the delayed perturbation of the two-parameter Mittag-Leffler type function and the delayed perturbation of the three-parameter Mittag-Leffler type function. We examine a couple of its properties in addition to identifying some of its relations with the existing Mittag-Leffler-type functions in the literature. We present an explicit formula by constructing on the general delayed perturbation of the three-parameter Mittag-Leffler type function as a solution to a linear fractional differential delayed equation with two distinct approaches.