Langevin differential equations with general fractional orders and their applications to electric circuit theory

Ahmadova A., Mahmudov N.

Journal of Computational and Applied Mathematics, vol.388, 2021 (SCI-Expanded, Scopus) identifier

  • Nəşrin Növü: Article / Article
  • Cild: 388
  • Nəşr tarixi: 2021
  • Doi nömrəsi: 10.1016/j.cam.2020.113299
  • jurnalın adı: Journal of Computational and Applied Mathematics
  • Jurnalın baxıldığı indekslər: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Computer & Applied Sciences, INSPEC, MathSciNet, Metadex, zbMATH, DIALNET, Civil Engineering Abstracts
  • Açar sözlər: Bivariate Mittag-Leffler functions, Caputo type fractional Langevin differential equations, Electrical circuits, Existence and uniqueness, Laplace transform, Ulam–Hyers stability
  • Açıq Arxiv Kolleksiyası: Məqalə
  • Adres: Yox

Qısa məlumat

Multi-order fractional differential equations have been studied due to their applications in modeling, and solved using various mathematical methods. We present explicit analytical solutions for several families of Langevin differential equations with general fractional orders, both homogeneous and inhomogeneous cases. The results can be written, in general and special cases, by means of a recently defined bivariate Mittag-Leffler function and the associated operators of fractional calculus. The novelty of this work is to apply an appropriate norm on the proof of existence and uniqueness theorem, and discuss the application of Langevin differential equation with fractional orders in several interesting cases to the electrical circuit. Moreover, we investigate Ulam–Hyers stability of Caputo type fractional Langevin differential equation. At the end, we provide an example to verify our main results.