ψ-Caputo type time-delay Langevin equations with two general fractional orders

Aydın M., Mahmudov E.

Mathematical Methods in the Applied Sciences, vol.46, no.8, pp.9187-9204, 2023 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 46 Issue: 8
  • Publication Date: 2023
  • Doi Number: 10.1002/mma.9047
  • Journal Name: Mathematical Methods in the Applied Sciences
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Compendex, INSPEC, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.9187-9204
  • Keywords: an explicit solution, existence uniqueness, Ulam-Hyers stability, ?-fractional Langevin equation, ?-delayed Mittag-Leffler function
  • Van Yüzüncü Yıl University Affiliated: Yes

Abstract

© 2023 John Wiley & Sons, Ltd.In the present paper, first, a (Formula presented.) -delayed Mittag–Leffler type function is introduced, which generalizes the existing delayed Mittag–Leffler type function. Second, by means of (Formula presented.) -delayed Mittag–Leffler type function, an exact analytical solution formula to non-homogeneous linear delayed Langevin equations involving two distinct (Formula presented.) -Caputo type fractional derivatives of general orders is obtained. Moreover, existence and uniqueness, stability of solution to nonlinear delayed Langevin fractional differential equations is obtained in the weighted space. Numerical and simulated examples are shared to exemplify the theoretical findings.