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Representations of Solutions of Time-Fractional Multi-Order Systems of Differential-Operator Equations.
- Source :
- Fractal & Fractional; May2024, Vol. 8 Issue 5, p254, 37p
- Publication Year :
- 2024
-
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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 25043110
- Volume :
- 8
- Issue :
- 5
- Database :
- Complementary Index
- Journal :
- Fractal & Fractional
- Publication Type :
- Academic Journal
- Accession number :
- 177497954
- Full Text :
- https://doi.org/10.3390/fractalfract8050254