Explicit analytical solutions of incommensurate fractional differential equation systems - Huseynov, Ismail T.; Ahmadova, Arzu; Fernandez, Arran; Mahmudov, Nazim I. (Elsevier Science Inc, 2021)
Fractional differential equations have been studied due to their applications in modelling, and solved using various mathematical methods. Systems of fractional differential equations are also used, for example in the study of electric circuits, but they are more difficult to analyse mathematically. We present explicit solutions for several families of such systems, both homogeneous and inhomogeneous cases, both commensurate and incommensurate. The results can be written, in several interesting special cases, in terms of a recently defined bivariate Mittag-Leffler function and the associated operators of fractional calculus. (C) 2020 Elsevier Inc. All rights reserved.
Keywords: Caputo fractional derivative; Fractional differential equation systems; Bivariate Mittag-Leffler functions; Incommensurate system