LAUSR

In this paper, a solution to initial value problems for fractional‐order linear commensurate multi‐term differential equations with Caputo derivatives is presented. The solution is obtained in the form of a finite sum of the Mittag‐Leffler–type functions and the meta‐trigonometric cosine function by using a numerical‐analytical method. The results of presented numerical experiments show that for high accuracy calculations of these functions, the multi‐precision arithmetic must be applied. The approach for solving of the initial value problems for generalized Basset equation, generalized Bagley‐Torvik equation, and multi‐term fractional equation is demonstrated.