Langevin delayed equations with Prabhakar derivatives involving two generalized fractional distinct orders


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Aydın M.

Turkish Journal of Mathematics, vol.48, no.2, pp.144-162, 2024 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 48 Issue: 2
  • Publication Date: 2024
  • Doi Number: 10.55730/1300-0098.3499
  • Journal Name: Turkish Journal of Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Page Numbers: pp.144-162
  • Keywords: Fractional Langevin type equation, Mittag-Leffler type function, Prabhakar fractional derivative, RLC circuit
  • Van Yüzüncü Yıl University Affiliated: Yes

Abstract

This paper is devoted to defining the delayed analogue of the Mittag-Leffler type function with three parameters and investigating a representation of a solution to Langevin delayed equations with Prabhakar derivatives involving two generalized fractional distinct orders, which are first introduced and investigated, by means of the Laplace integral transform. It is verified by showing the solution satisfies the introduced system. Special cases which are also novel are presented as examples. The findings are illustrated with the help of the RLC circuits.