This paper reports the innovative results on the stability and bifurcation for a delayed
fractional-order quaternion-valued neural network (FOQVNN). Delay-stimulated bifurcation …

In this paper, we obtain some basic results of quaternion algorithms and quaternion calculus
on time scales. Based on this, a Liouville formula and some related properties are derived …

This paper deals with the stability of linear quaternion-valued differential equations. First, we
derive an explicit norm estimation like the matrix exponential function in the sense of …

In this paper, we transfer the approach of finding the explicit solutions to linear impulsive
differential equations (LIDEs) to quaternion-valued case. We develop the similar idea to find …

Quaternion is a four-dimensional and an extension of the complex number system. It is often
viewed from various fields, such as analysis, algebra, and geometry. Several applications of …

In this paper, the controllability and observability for linear quaternion-valued impulsive
differential equations (QIDEs) are investigated. We mainly establish some sufficient and …

The main focus of this study is on the relative controllability of linear and semilinear
quaternion differential equations with delay. The Gram criterion and the rank criterion for the …

Since the non-commutativity and particular structure of the quaternion algebra, the quternion
difference equations (short for QDCEs) have a large difference from the classical theory of …

Hyers–Ulam stability for linear quaternion-valued differential equations with constant
coefficient Page 1 ROCKY MOUNTAIN JOURNAL OF MATHEMATICS Volume 52 (2022) …

In this paper, linear quaternion differential equations (LQDEs) with delay attracts our
attention. In the light of delayed quaternion matrix exponential and the method of variation of …