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A numerical‐analytical solution of multi‐term fractional‐order differential equations
Author(s) -
Kukla Stanisław,
Siedlecka Urszula
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6242
Subject(s) - mathematics , term (time) , trigonometric functions , differential equation , mathematical analysis , trigonometry , fractional calculus , initial value problem , order (exchange) , function (biology) , numerical analysis , physics , finance , quantum mechanics , economics , geometry , evolutionary biology , biology
In this paper, a solution to initial value problems for fractional‐order linear commensurate multi‐term differential equations with Caputo derivatives is presented. The solution is obtained in the form of a finite sum of the Mittag‐Leffler–type functions and the meta‐trigonometric cosine function by using a numerical‐analytical method. The results of presented numerical experiments show that for high accuracy calculations of these functions, the multi‐precision arithmetic must be applied. The approach for solving of the initial value problems for generalized Basset equation, generalized Bagley‐Torvik equation, and multi‐term fractional equation is demonstrated.