Analytic study on linear systems of distributed order fractional differential equations

In this paper we introduce the distributed order fractional differential equations (DOFDE) with respect to the nonnegative density function. We generalize the inertia and characteristics polynomial concepts of pair $(A,B)$ with respect to the nonnegative density function. We also give generalization of the invariant factors of a matrix and some inertia theorems for analyzing the stability of the DOFDE systems.