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Fractional calculus has been found to be a very useful tool for modeling linear systems. In this paper, a method for computation of a set of a minimal positive realization of a given transfer function of linear fractional continuous-time descriptor systems has been presented. The proposed method is based on digraph theory. Also, two cases of a possible input-output digraph structure are investigated and discussed. It should be noted that a digraph mask is introduced and used for the first time to solve a minimal positive realization problem. For the presented method, an algorithm was also constructed. The proposed solution allows minimal digraph construction for any one-dimensional fractional positive system. The proposed method is discussed and illustrated in detail with some numerical examples.<\/jats:p>","DOI":"10.2478\/amcs-2018-0001","type":"journal-article","created":{"date-parts":[[2018,3,31]],"date-time":"2018-03-31T22:16:18Z","timestamp":1522534578000},"page":"9-24","source":"Crossref","is-referenced-by-count":4,"title":["Minimal positive realizations of linear continuous-time fractional descriptor systems: Two cases of an input-output digraph structure"],"prefix":"10.61822","volume":"28","author":[{"given":"Konrad Andrzej","family":"Markowski","sequence":"first","affiliation":[{"name":"Institute of Control and Industrial Electronics, Faculty of Electrical Engineering Warsaw University of Technology, Koszykowa 75, 00-662 Warsaw , Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"37438","published-online":{"date-parts":[[2018,3,31]]},"reference":[{"key":"2023050302340507579_j_amcs-2018-0001_ref_001_w2aab3b7ab1b6b1ab1ab1Aa","doi-asserted-by":"crossref","unstructured":"Bang-Jensen, J. and Gutin, G. 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