Sharif University of TechnologyScientia Iranica1026-309827320200601Analytic solution of a system of linear distributed order differential equations in the Reimann-Liouville sense138413972033510.24200/sci.2018.20335ENHamedTaghavianDepartment of Electrical Engineering Sharif University of Technology, Tehran, IranMohammad SalehTavazoeiDepartment of Electrical Engineering Sharif University of Technology, Tehran, IranJournal Article20160817In 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.http://scientiairanica.sharif.edu/article_20335_9c3fff9bfa849d410a81a373581c7bfb.pdf