Author URLs
Document Type
Article
Publication Date
5-2024
Subject: LCSH
Fractional calculus, Cauchy problem--Numerical solutions
Disciplines
Mathematics
Abstract
This paper is devoted to the general theory of systems of linear time-fractional differential-operator equations. The representation formulas for solutions of systems of ordinary differential equations with single (commensurate) fractional order is known through the matrix-valued Mittag-Leffler function. Multi-order (incommensurate) systems with rational components can be reduced to single-order systems, and, hence, representation formulas are also known. However, for arbitrary fractional multi-order (not necessarily with rational components) systems of differential equations, the representation formulas are still unknown, even in the case of fractional-order ordinary differential equations. In this paper, we obtain representation formulas for the solutions of arbitrary fractional multi-order systems of differential-operator equations. The existence and uniqueness theorems in appropriate topological vector spaces are also provided. Moreover, we introduce vector-indexed Mittag-Leffler functions and prove some of their properties.
DOI
https://doi.org/10.3390/fractalfract8050254
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Repository Citation
Umarov, Sabir, "Representations of Solutions of Time-Fractional Multi-Order Systems of Differential-Operator Equations" (2024). Mathematics Faculty Publications. 22.
https://digitalcommons.newhaven.edu/mathematics-facpubs/22
Publisher Citation
Umarov, S. Representations of Solutions of Time-Fractional Multi-Order Systems of Differential-Operator Equations. Fractal Fract. 2024, 8, 254. https://doi.org/10.3390/fractalfract8050254
Comments
This article was originally published in, "Fractal and Fractional," volume 8, issue 5.