Multi-delayed perturbation of Mittag-Leffler type matrix functions. (English) Zbl 1486.34156
The author first introduces a multivariate determining function and proposes a multi-delayed perturbation of the Mittag-Leffler type matrix function. It is an extension of the classical delayed exponential and Mittag-Leffler type matrix functions.
This paper completes the study of the exact analytic representation of solutions to linear constant matrix coefficient systems of Riemann-Liouville differential equations with multiple delays of higher order \(l-1<\alpha\leq l\), \(l\in \mathbb{N}\).
The author constructs a simple explicit solution that is valid in homogeneous and inhomogeneous cases.
The construction of the exact analytical solution requires the use of a newly established multi-delayed Mittag-Leffler function.
This paper completes the study of the exact analytic representation of solutions to linear constant matrix coefficient systems of Riemann-Liouville differential equations with multiple delays of higher order \(l-1<\alpha\leq l\), \(l\in \mathbb{N}\).
The author constructs a simple explicit solution that is valid in homogeneous and inhomogeneous cases.
The construction of the exact analytical solution requires the use of a newly established multi-delayed Mittag-Leffler function.
Reviewer: Ismail Huseynov (Mersin)
MSC:
| 34K37 | Functional-differential equations with fractional derivatives |
| 34K06 | Linear functional-differential equations |
| 33E12 | Mittag-Leffler functions and generalizations |
| 44A10 | Laplace transform |
Keywords:
Mittag-Leffler type matrix function; multi-delay equations; delayed Mittag-Leffler type function; Laplace transformReferences:
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