{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,14]],"date-time":"2025-05-14T02:52:23Z","timestamp":1747191143812,"version":"3.40.5"},"reference-count":24,"publisher":"Wiley","license":[{"start":{"date-parts":[[2023,3,16]],"date-time":"2023-03-16T00:00:00Z","timestamp":1678924800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Complexity"],"published-print":{"date-parts":[[2023,3,16]]},"abstract":"<jats:p>In this study, Lane\u2013Emden complex differential equations have been randomized by selecting random variables for the coefficients, initial conditions, and force functions of complex differential equations. In addition, by finding the solutions of the obtained random complex differential equations, the probability characteristics of the solutions are examined. The random version of the differential transformation method (DTM) is used to obtain an analytical solution close to the solution of the random differential equation. Approximate expected values and variances are calculated using the approximate solution method. The solutions of some random complex differential equations obtained by using random probability characteristics with gamma, normal, and beta distributions were obtained by the DTM method. The probability characteristics obtained are shown graphically with the help of the MAPLE program.<\/jats:p>","DOI":"10.1155\/2023\/3713454","type":"journal-article","created":{"date-parts":[[2023,3,16]],"date-time":"2023-03-16T17:51:12Z","timestamp":1678989072000},"page":"1-12","source":"Crossref","is-referenced-by-count":1,"title":["Investigation of Behavior on Solutions of Lane\u2013Emden Complex Differential Equations by a Random Differential Transformation Method"],"prefix":"10.1155","volume":"2023","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8509-3044","authenticated-orcid":true,"given":"Mehmet","family":"Merdan","sequence":"first","affiliation":[{"name":"Department of Mathematical Engineering, G\u00fcm\u00fc\u015fhane University, G\u00fcm\u00fc\u015fhane, Turkey"}]},{"given":"Merve","family":"Merdan","sequence":"additional","affiliation":[{"name":"Department of Mathematical Engineering, G\u00fcm\u00fc\u015fhane University, G\u00fcm\u00fc\u015fhane, Turkey"}]},{"given":"R\u0131dvan","family":"\u015eahin","sequence":"additional","affiliation":[{"name":"Department of Mathematical Engineering, G\u00fcm\u00fc\u015fhane University, G\u00fcm\u00fc\u015fhane, Turkey"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.1016\/s0096-3003(99)00223-4"},{"volume-title":"Differential Transformation and its Applications for Electrical Circuits","year":"1986","author":"J. K. Zhou","key":"2"},{"key":"3","first-page":"69","article-title":"The differential transform methods for nonlinear functions and its applications","volume":"9","author":"Y. Keskin","year":"2008","journal-title":"Sel\u00e7uk Journal of Applied Mathematics"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1016\/s0096-3003(02)00368-5"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1016\/s0096-3003(97)10096-0"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1016\/s0096-3003(03)00723-9"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1016\/s0096-3003(98)10115-7"},{"volume-title":"Theory of Pseudo-analytic Functions","year":"1953","author":"L. Bers","key":"8"},{"volume-title":"Verallgemeinerte Analytische Funktionen","year":"1959","author":"I. N. Vekua","key":"9"},{"issue":"2","key":"10","first-page":"179","article-title":"Using two-dimensional differential transform to solve second order complex partial differential equations","volume":"7","author":"M. D\u00fcz","year":"2014","journal-title":"European Journal of Pure and Applied Mathematics"},{"key":"11","first-page":"221","article-title":"Solution of second order complex equations with Adomian decomposition method","volume":"8","author":"M. D\u00fcz","year":"2018","journal-title":"Bulletin of the International Mathematical Virtual Institute"},{"key":"12","first-page":"145","article-title":"Using two dimensional differential transform method solve of third order complex differential equations","volume":"5","author":"M. D\u00fcz","year":"2016","journal-title":"Palestine Journal of Mathematics"},{"key":"13","first-page":"66","article-title":"Solution of complex differential equation system by using differential transform method","volume":"14","author":"M. D\u00fcz","year":"2014","journal-title":"Global Journal of Science Frontier Research: F Mathematics and Decision Sciences"},{"issue":"1","key":"14","first-page":"66","article-title":"Solution of complex equations with adomian decomposition method","volume":"7","author":"M. D\u00fcz","year":"2017","journal-title":"TWMS Journal of Applied and Engineering Mathematics"},{"volume-title":"Introduction to Nonlinear Differential and Integral Equations","year":"1962","author":"H. T. Davis","key":"15"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.2475\/ajs.s2-50.148.57"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.2475\/ajs.s2-50.148.57"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.17714\/gumusfenbil.404332"},{"issue":"3","key":"19","first-page":"1269","article-title":"Analys\u0131s of random d\u0131screte t\u0131me log\u0131st\u0131c model","volume":"38","author":"M. Merdan","year":"2020","journal-title":"Sigma Journal of Engineering and Natural Sciences Sigma"},{"key":"20","doi-asserted-by":"publisher","DOI":"10.17714\/gumusfenbil.586796"},{"key":"21","unstructured":"MerdanM.Ordinary and partial complex differential equations with random effects2020G\u00fcm\u00fc\u015fhane, T\u00fcrkiyeG\u00fcm\u00fc\u015fhane University Institute of Science and TechnologyMaster\u2019s Thesis"},{"key":"22","volume-title":"An Introduction to Probability Theory and its Applications","author":"W. Feller","year":"1968","edition":"3rd"},{"issue":"3","key":"23","first-page":"115","article-title":"Multi-step stochastic differential transformation method for solving some class of random differential equations","volume":"3","author":"J. Fakharzadeh","year":"2015","journal-title":"Applied Mathematics in Engineering, Management and Technology"},{"issue":"2","key":"24","first-page":"350","article-title":"Mean square solutions of second-order random differential equations by using homotopy analysis method","volume":"65","author":"A. K. Golmankhaneh","year":"2013","journal-title":"Romanian Reports in Physics"}],"container-title":["Complexity"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2023\/3713454.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2023\/3713454.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2023\/3713454.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,3,16]],"date-time":"2023-03-16T17:51:27Z","timestamp":1678989087000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.hindawi.com\/journals\/complexity\/2023\/3713454\/"}},"subtitle":[],"editor":[{"given":"Lucia Valentina","family":"Gambuzza","sequence":"additional","affiliation":[]}],"short-title":[],"issued":{"date-parts":[[2023,3,16]]},"references-count":24,"alternative-id":["3713454","3713454"],"URL":"https:\/\/doi.org\/10.1155\/2023\/3713454","relation":{},"ISSN":["1099-0526","1076-2787"],"issn-type":[{"type":"electronic","value":"1099-0526"},{"type":"print","value":"1076-2787"}],"subject":[],"published":{"date-parts":[[2023,3,16]]}}}