%0 Journal Article
%T Analytic solution of a system of linear distributed order differential equations in the Reimann-Liouville sense
%J Scientia Iranica
%I Sharif University of Technology
%Z 1026-3098
%A Taghavian, Hamed
%A Tavazoei, Mohammad Saleh
%D 2020
%\ 06/01/2020
%V 27
%N 3
%P 1384-1397
%! Analytic solution of a system of linear distributed order differential equations in the Reimann-Liouville sense
%K Analytic solution
%K distributed order differential equation
%K Reimann-Liouville fractional derivative
%K Mittag-Leffler function
%K relaxation process
%R 10.24200/sci.2018.20335
%X In this paper, solution of a system of linear differential equations of distributed order in the Riemann-Liouville sense is analytically obtained. The distributed order relaxation equation is a special case of the system investigated in this paper. The solution of the mentioned system is introduced on the basis of a function which can be considered as the distributed order generalization of the matrix Mittag-Leffler functions. It is shown that this generalized function in two special cases of the weight function can be expressed in terms of the multivariate Mittag-Leffler functions and the Wright functions.
%U http://scientiairanica.sharif.edu/article_20335_9c3fff9bfa849d410a81a373581c7bfb.pdf