The exponential of a constant matrix on time scales

Abstract

In this paper we describe an elementary method for calculating the matrix exponential on an arbitrary time scale. An example is also given to illustrate the result.2000 Mathematics subject classification: primary 34A30.

Principal Matrix Solutions and Variation of Parameters for Volterra Integro-Dynamic Equations on Time Scales

“…For more on matrix exponential on time scales, we refer to [4,Section 5] and [19] and references therein).…”

Existence of Resolvent for Volterra Integral Equations on Time Scales

“…and hence the delta derivative turns into an ordinary derivative if T = R and it becomes the forward difference operator for T = Z. It is evident from various papers (see [1,5,6,12] and references therein) that dynamic equations on time scales are useful tools to explain the differences and similarities between difference and differential equations. Providing a wide perspective, the theory of time scales also leads to some new results for both the discrete and continuous cases.…”