Analytic Solution of a System of Linear Distributed Order Differential Equations in the Reimann-Liouville Sense

Document Type: Article

Authors

Electrical Engineering Department, Sharif University of Technology, Tehran, Iran

Abstract

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.

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