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Peer-reviewedCC BY 4.0Mathematics

Novel Fractional Delayed Mittag-Leffler-Type Matrices and Their Applications Without Commutativity Constraints

  • Ahmed M. Elshenhab1
  • Ghada AlNemer2
  • Amirah M. Alharthi3
  • Xing Tao Wang4
4 affiliations
  1. 1Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
  2. 2Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
  3. 3Department of Mathematics, Faculty of Science, University of Bisha, Bisha 61922, Saudi Arabia
  4. 4School of Mathematics, Harbin Institute of Technology, Harbin 150001, China
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Abstract

A general analytical scheme for solving fractional delay differential two-sided matrix equations without imposing any commutativity between the coefficient matrices, inhomogeneity, and initial values is established. Generalized binomial expansions together with new fractional delayed Mittag-Leffler-type matrix functions are proposed and used to derive solutions for the non-homogeneous equations in closed form. The proposed approach encompasses a general solution approach for understanding peculiar behavior of systems in which the effect of initial conditions and inhomogeneity are noncommutative in nature. Furthermore, the Hyers–Ulam stability of the system is studied, and the solutions are stable with respect to bounded perturbations. Lastly, numerical examples are given for demonstrating the behavior of solutions and the validity of the stability results. The method posed settles a number of open issues of fractionalization of matrix differential delay equations.

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Cite

BibTeXRIS
BibTeX
@article{elshenhab2026novel,
  title = {{Novel Fractional Delayed Mittag-Leffler-Type Matrices and Their Applications Without Commutativity Constraints}},
  author = {Ahmed M. Elshenhab and Ghada AlNemer and Amirah M. Alharthi and Xing Tao Wang},
  journal = {Mathematics},
  year = {2026},
  month = oct,
  doi = {10.3390/math14213878},
  url = {https://www.mdpi.com/2227-7390/14/21/3878},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Novel Fractional Delayed Mittag-Leffler-Type Matrices and Their Applications Without Commutativity Constraints
AU  - Ahmed M. Elshenhab
AU  - Ghada AlNemer
AU  - Amirah M. Alharthi
AU  - Xing Tao Wang
PY  - 2026
DA  - 2026/10/24
JO  - Mathematics
DO  - 10.3390/math14213878
UR  - https://www.mdpi.com/2227-7390/14/21/3878
AB  - A general analytical scheme for solving fractional delay differential two-sided matrix equations without imposing any commutativity between the coefficient matrices, inhomogeneity, and initial values is established. Generalized binomial expansions together with new fractional delayed Mittag-Leffler-type matrix functions are proposed and used to derive solutions for the non-homogeneous equations in closed form. The proposed approach encompasses a general solution approach for understanding peculiar behavior of systems in which the effect of initial conditions and inhomogeneity are noncommutative in nature. Furthermore, the Hyers–Ulam stability of the system is studied, and the solutions are stable with respect to bounded perturbations. Lastly, numerical examples are given for demonstrating the behavior of solutions and the validity of the stability results. The method posed settles a number of open issues of fractionalization of matrix differential delay equations.
SN  - 2227-7390
ER  -