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We study nonhomogeneous systems of linear conformable fractional differential equations with pure delay. By using new conformable delayed matrix functions and the method of variation, we obtain a representation of their solutions. As an application, we derive a finite time stability result using the representation of solutions and a norm estimation of the conformable delayedmatrix functions. The obtained results are new, and they extend and improve some existing ones. Finally, an example is presented to illustrate the validity of our theoretical results. [ABSTRACT FROM AUTHOR]

Linear and nonlinear fractional-delay systems are studied. As an application, we derive the controllability and Hyers–Ulam stability results using the representation of solutions of these systems with the help of their delayed Mittag–Leffler matrix functions. We provide some sufficient and necessary conditions for the controllability of linear fractional-delay systems by introducing a fractional delay Gramian matrix. Furthermore, we establish some sufficient conditions of controllability and Hyers–Ulam stability of nonlinear fractional-delay systems by applying Krasnoselskii's fixed-point theorem. Our results improve, extend, and complement some existing ones. Finally, numerical examples of linear and nonlinear fractional-delay systems are presented to demonstrate the theoretical results. [ABSTRACT FROM AUTHOR]

Nonhomogeneous systems governed by second-order linear differential equations with pure delay are considered. As an application, the exact solutions of these systems and their delayed matrix functions are used to obtain the finite-time stability results. Our results extend and improve some previous results by removing some restrictive conditions. Finally, an example is provided to illustrate our theoretical results. [ABSTRACT FROM AUTHOR]

Nonhomogeneous systems of linear fractional equations with pure delay and multiple delays with linear parts given by permutable or nonpermutable matrices are considered. Representations of their solutions are obtained by using delayed Mittag–Leffler type matrix functions and Laplace transform. Our results are new and extend previous results. [ABSTRACT FROM AUTHOR]

• Nonhomogeneous linear systems of second order differential equations with pure delay and multiple delays are considered. • Representations of their solutions without a commutativity assumption on the matrix coefficients are obtained by using delayed matrix functions and Laplace transform. • Our results improve and extend previous results. Nonhomogeneous linear systems of second order differential equations with pure delay and multiple delays are considered. Representations of their solutions without a commutativity assumption on the matrix coefficients are obtained by using delayed matrix functions and Laplace transform. Our results improve and extend previous results. [ABSTRACT FROM AUTHOR]