Representation of Solutions and Ulam–Hyers Stability of the Two-Sided Fractional Matrix Delay Differential Equations

This paper investigates linear two-sided fractional matrix delay differential equations (TSFMDDE). Firstly, the two-sided fractional delayed Mittag-Leffler matrix functions (TSFDMLMF) are constructed. Further, the representation of solutions of two-sided homogeneous and nonhomogeneous problems are studied, and Ulam–Hyers (UH) stability of a two-sided nonhomogeneous problem is discussed. Lastly, we provide a numerical example to demonstrate our results. In the numerical example, the fractional order β=0.6, delay ϱ=2, UH constant uh≈5.92479, n=2, and s∈[−2,4].