Multi-Delayed Discrete Matrix Functions and Their Applications in Solving Higher-Order Difference Equations

Ahmed M. Elshenhab (), Ghada AlNemer and Xing Tao Wang
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Ahmed M. Elshenhab: Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
Ghada AlNemer: Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
Xing Tao Wang: School of Mathematics, Harbin Institute of Technology, Harbin 150001, China

Mathematics, 2025, vol. 13, issue 18, 1-16

Abstract: A new class of linear non-homogeneous discrete matrix equations with multiple delays and second-order differences is considered, where the coefficient matrices satisfy pairwise permutability conditions. First, new multi-delayed discrete matrix sine- and cosine-type functions are introduced, which generalize existing delayed discrete matrix functions. Based on the introduced matrix functions and appropriate commutativity conditions, an explicit matrix representation of the solution is derived. The importance of our results is shown by comparing them with related previous works, along with suggestions about some new open problems. Finally, an example is provided to illustrate the importance of the results.

Keywords: second-order difference; discrete matrix equation; multiple delays; multi-delayed discrete matrix functions; exact solutions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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