LAUSR

Abstract Matrices have important applications of statistical analysis, circuits, mechanics, optics, and quantum physics. In this article, matrix explicit formulas of the exponentials for computing exp(αA), where A is a special n × n matrix and α is the order of fractional derivative, were obtained. The definitions of the fractional derivative respectively are the Caputo fractional derivative and Riemann-Liouville fractional derivative. Here, we need to point that the new results can be looked as an extended the previous work of the authors. The explicit formulas can help us better to explore deep connotations from natural science.