{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:41:07Z","timestamp":1760197267921,"version":"build-2065373602"},"reference-count":38,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2018,5,23]],"date-time":"2018-05-23T00:00:00Z","timestamp":1527033600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>This paper introduces a general solution of singular fractional-order linear-time invariant (FoLTI) continuous systems using the Adomian Decomposition Method (ADM) based on the Caputo's definition of the fractional-order derivative. The complexity of their entropy lies in defining the complete solution of such systems, which depends on introducing a method of decomposing their dynamic states from their static states. The solution is formulated by converting the singular system of regular pencils into a recursive form using the sequence of transformations, which separates the dynamic variables from the algebraic variables. The main idea of this work is demonstrated via numerical examples.<\/jats:p>","DOI":"10.3390\/e20060400","type":"journal-article","created":{"date-parts":[[2018,5,24]],"date-time":"2018-05-24T02:55:43Z","timestamp":1527130543000},"page":"400","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":22,"title":["The General Solution of Singular Fractional-Order Linear Time-Invariant Continuous Systems with Regular Pencils"],"prefix":"10.3390","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8443-8848","authenticated-orcid":false,"given":"Iqbal M.","family":"Batiha","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science, University of Jordan, Amman 11942, Jordan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3205-7477","authenticated-orcid":false,"given":"Reyad","family":"El-Khazali","sequence":"additional","affiliation":[{"name":"ECCE Department, Khalifa University, Abu-Dhabi 127788, United Arab Emirates"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ahmed","family":"AlSaedi","sequence":"additional","affiliation":[{"name":"Department of Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Faculty of Science, King Abdulaziz University (KAU), Jeddah 21589, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6326-8456","authenticated-orcid":false,"given":"Shaher","family":"Momani","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, University of Jordan, Amman 11942, Jordan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,5,23]]},"reference":[{"key":"ref_1","unstructured":"Das, S. 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