Trivariate Mittag-Leffler functions used to solve multi-order systems of fractional differential equations
| Autor: | Arzu Ahmadova, Ismail T. Huseynov, Nazim I. Mahmudov, Arran Fernandez |
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| Rok vydání: | 2021 |
| Předmět: |
Numerical Analysis
Laplace transform Series (mathematics) Explicit formulae Applied Mathematics Numerical analysis Linear system Function (mathematics) 01 natural sciences 010305 fluids & plasmas Fractional calculus Matrix (mathematics) Modeling and Simulation 0103 physical sciences Applied mathematics 010306 general physics Mathematics |
| Zdroj: | Communications in Nonlinear Science and Numerical Simulation. 97:105735 |
| ISSN: | 1007-5704 |
| DOI: | 10.1016/j.cnsns.2021.105735 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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