TY - JOUR
ID - 20335
TI - Analytic solution of a system of linear distributed order differential equations in the Reimann-Liouville sense
JO - Scientia Iranica
JA - SCI
LA - en
SN - 1026-3098
AU - Taghavian, Hamed
AU - Tavazoei, Mohammad Saleh
AD - Department of Electrical Engineering Sharif University of Technology, Tehran, Iran
Y1 - 2020
PY - 2020
VL - 27
IS - 3
SP - 1384
EP - 1397
KW - Analytic solution
KW - distributed order differential equation
KW - Reimann-Liouville fractional derivative
KW - Mittag-Leffler function
KW - relaxation process
DO - 10.24200/sci.2018.20335
N2 - 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.
UR - http://scientiairanica.sharif.edu/article_20335.html
L1 - http://scientiairanica.sharif.edu/article_20335_9c3fff9bfa849d410a81a373581c7bfb.pdf
ER -