Trivariate Mittag-Leffler functions used to solve multi-order systems of fractional differential equations

Ahmadova A., Huseynov I. T., Fernandez A., Mahmudov N.

Communications in Nonlinear Science and Numerical Simulation, vol.97, 2021 (SCI-Expanded, Scopus) identifier

  • Nəşrin Növü: Article / Article
  • Cild: 97
  • Nəşr tarixi: 2021
  • Doi nömrəsi: 10.1016/j.cnsns.2021.105735
  • jurnalın adı: Communications in Nonlinear Science and Numerical Simulation
  • Jurnalın baxıldığı indekslər: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Aquatic Science & Fisheries Abstracts (ASFA), Communication Abstracts, Compendex, INSPEC, Metadex, zbMATH, Civil Engineering Abstracts
  • Açar sözlər: Caputo fractional derivative, Differential equation systems, Fractional calculus, Fractional differential equations, Laplace transform, Trivariate Mittag-Leffler functions
  • Açıq Arxiv Kolleksiyası: Məqalə
  • Adres: Yox

Qısa məlumat

Linear systems of fractional differential equations have been studied from various points of view: applications to electric circuit theory, approximate solutions by numerical methods, and recently exact solutions by analytical methods. We discover here that, to obtain a fully closed-form solution in all cases, it is necessary to introduce a new type of Mittag-Leffler function involving triple series, and also to construct the associated fractional calculus operators, which we introduce and study in this paper. We then complete the rigorous analytical solutions for the aforesaid systems of fractional differential equations. As a consequence, comparing the solutions found here with the vector-matrix solutions known in the literature, we obtain explicit formulae for the elements of the 2×2 matrix Mittag-Leffler function.