Fractional Langevin type delay equations with two fractional derivatives

Mahmudov N.

Applied Mathematics Letters, vol.103, 2020 (SCI-Expanded, Scopus)

  • Publication Type: Article / Article
  • Volume: 103
  • Publication Date: 2020
  • Doi Number: 10.1016/j.aml.2020.106215
  • Journal Name: Applied Mathematics Letters
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Compendex, INSPEC, MathSciNet, zbMATH, Civil Engineering Abstracts
  • Keywords: Fractional Langevin type equation, Mittag-Leffler type function
  • Open Archive Collection: Article
  • Azerbaijan State University of Economics (UNEC) Affiliated: No

Abstract

In this article, a delayed Mittag-Leffler type function is introduced. With the help of delayed Mittag-Leffler type functions, we give an explicit solution formula to linear non-homogeneous fractional delayed Langevin equations containing two Riemann–Liouville fractional derivatives. Estimation for delayed Mittag-Leffler type function in terms of exponential function is given. Existence uniqueness and Ulam-Hyers stability of solutions are obtained in terms of weighted norms.