Next Article in Journal
Correction: Çakmak, A. New Type Direction Curves in 3-Dimensional Compact Lie Group Symmetry 2019, 11, 387
Previous Article in Journal
A Privacy-Protected Image Retrieval Scheme for Fast and Secure Image Search
Previous Article in Special Issue
A Fast and Exact Greedy Algorithm for the Core–Periphery Problem
Open AccessArticle

General Solutions for Descriptor Systems of Coupled Generalized Sylvester Matrix Fractional Differential Equations via Canonical Forms

Department of Mathematics, Faculty of Science, King Mongkut’s Institute of Technology Ladkrabang, Bangkok 10520, Thailand
*
Author to whom correspondence should be addressed.
Symmetry 2020, 12(2), 283; https://doi.org/10.3390/sym12020283 (registering DOI)
Received: 24 January 2020 / Revised: 7 February 2020 / Accepted: 8 February 2020 / Published: 14 February 2020
(This article belongs to the Special Issue Symmetry in Numerical Linear and Multilinear Algebra)
We investigate a descriptor system of coupled generalized Sylvester matrix fractional differential equations in both non-homogeneous and homogeneous cases. All fractional derivatives considered here are taken in Caputo’s sense. We explain a 4-step procedure to solve the descriptor system, consisting of vectorization, a matrix canonical form concerning ranks, and matrix partitioning. The procedure aims to reduce the descriptor system to a descriptor system of fractional differential equations. We also impose a condition on coefficient matrices, related to the symmetry of the solution for descriptor systems. It follows that an explicit form of its general solution is given in terms of matrix power series concerning Mittag–Leffler functions. The main system includes certain systems of coupled matrix/vector differential equations, and single matrix differential equations as special cases. In particular, we obtain an alternative procedure to solve linear continuous-time descriptor systems via a matrix canonical form. View Full-Text
Keywords: descriptor system; linear fractional differential equation; Caputo’s derivative; Kronecker product; vector operator; Mittag–Leffler function descriptor system; linear fractional differential equation; Caputo’s derivative; Kronecker product; vector operator; Mittag–Leffler function
MDPI and ACS Style

Tansri, K.; Chansangiam, P. General Solutions for Descriptor Systems of Coupled Generalized Sylvester Matrix Fractional Differential Equations via Canonical Forms. Symmetry 2020, 12, 283.

Show more citation formats Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Back to TopTop