Amir Sadeghi - Department of Mathematics, Islamic Azad University, Robat Karim Branch, Tehran, Iran
Maryam Shams Solary - Department of Mathematics, Payame Noor University, P.O. Box ۱۹۳۹۵-۳۶۹۷, Tehran, Iran

It is well known that the matrix exponential function has practical applications in engineering and applied sciences. In this paper, we present some new explicit identities to the exponential functions of a special class of matrices that are known as central-symmetric X-form. For instance, e^{\mathbf{A}t}, t^{\mathbf{A}} and a^{\mathbf{A}t} will be evaluated by the new formulas in this particular structure. Moreover, upper bounds for the explicit relations will be given via subordinate matrix norms. Eventually, some numerical illustrations and applications are also adapted.

central-symmetric matrix, matrix function, matrix exponential, Gamma and Beta matrix functions