A Vectorization Approach to Solving and Controlling Fractional Delay Differential Sylvester Systems

Fatemah Mofarreh and Ahmed M. Elshenhab ()
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Fatemah Mofarreh: Mathematical Science Department, Faculty of Science, Princess Nourah Bint Abdulrahman University, Riyadh 11546, Saudi Arabia
Ahmed M. Elshenhab: Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt

Mathematics, 2025, vol. 13, issue 22, 1-17

Abstract: This paper addresses the solvability and controllability of fractional delay differential Sylvester matrix equations with non-permutable coefficient matrices. By applying a vectorization approach and Kronecker product algebra, we transform the matrix-valued problem into an equivalent vector system, enabling the derivation of explicit solution representations using a delayed perturbation of two-parameter Mittag-Leffler-type matrix functions. We establish necessary and sufficient conditions for controllability via a fractional delay Gramian matrix, providing a computationally verifiable criterion that requires no commutativity assumptions. The theoretical results are validated through numerical examples, demonstrating effectiveness in noncommutative scenarios where classical methods fail.

Keywords: representation of solutions; fractional delay differential Sylvester matrix equation; delayed perturbation matrix function; controllability; Kronecker product; vector operator (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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