{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,13]],"date-time":"2026-04-13T19:34:21Z","timestamp":1776108861543,"version":"3.50.1"},"reference-count":44,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2023,4,24]],"date-time":"2023-04-24T00:00:00Z","timestamp":1682294400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["12272064"],"award-info":[{"award-number":["12272064"]}]},{"name":"National Natural Science Foundation of China","award":["12101086"],"award-info":[{"award-number":["12101086"]}]},{"name":"National Natural Science Foundation of China","award":["CJ20220238"],"award-info":[{"award-number":["CJ20220238"]}]},{"name":"National Natural Science Foundation of China","award":["CE20215057"],"award-info":[{"award-number":["CE20215057"]}]},{"name":"National Natural Science Foundation of China","award":["CZ20220030"],"award-info":[{"award-number":["CZ20220030"]}]},{"name":"National Natural Science Foundation of China","award":["CQ20220092"],"award-info":[{"award-number":["CQ20220092"]}]},{"name":"National Natural Science Foundation of China","award":["22KJA580001"],"award-info":[{"award-number":["22KJA580001"]}]},{"name":"Changzhou Science and technology planning project","award":["12272064"],"award-info":[{"award-number":["12272064"]}]},{"name":"Changzhou Science and technology planning project","award":["12101086"],"award-info":[{"award-number":["12101086"]}]},{"name":"Changzhou Science and technology planning project","award":["CJ20220238"],"award-info":[{"award-number":["CJ20220238"]}]},{"name":"Changzhou Science and technology planning project","award":["CE20215057"],"award-info":[{"award-number":["CE20215057"]}]},{"name":"Changzhou Science and technology planning project","award":["CZ20220030"],"award-info":[{"award-number":["CZ20220030"]}]},{"name":"Changzhou Science and technology planning project","award":["CQ20220092"],"award-info":[{"award-number":["CQ20220092"]}]},{"name":"Changzhou Science and technology planning project","award":["22KJA580001"],"award-info":[{"award-number":["22KJA580001"]}]},{"name":"Changzhou Leading Innovative Talents Cultivation Project","award":["12272064"],"award-info":[{"award-number":["12272064"]}]},{"name":"Changzhou Leading Innovative Talents Cultivation Project","award":["12101086"],"award-info":[{"award-number":["12101086"]}]},{"name":"Changzhou Leading Innovative Talents Cultivation Project","award":["CJ20220238"],"award-info":[{"award-number":["CJ20220238"]}]},{"name":"Changzhou Leading Innovative Talents Cultivation Project","award":["CE20215057"],"award-info":[{"award-number":["CE20215057"]}]},{"name":"Changzhou Leading Innovative Talents Cultivation Project","award":["CZ20220030"],"award-info":[{"award-number":["CZ20220030"]}]},{"name":"Changzhou Leading Innovative Talents Cultivation Project","award":["CQ20220092"],"award-info":[{"award-number":["CQ20220092"]}]},{"name":"Changzhou Leading Innovative Talents Cultivation Project","award":["22KJA580001"],"award-info":[{"award-number":["22KJA580001"]}]},{"name":"major project of Basic science (Natural science) research in colleges and universities of Jiangsu Province","award":["12272064"],"award-info":[{"award-number":["12272064"]}]},{"name":"major project of Basic science (Natural science) research in colleges and universities of Jiangsu Province","award":["12101086"],"award-info":[{"award-number":["12101086"]}]},{"name":"major project of Basic science (Natural science) research in colleges and universities of Jiangsu Province","award":["CJ20220238"],"award-info":[{"award-number":["CJ20220238"]}]},{"name":"major project of Basic science (Natural science) research in colleges and universities of Jiangsu Province","award":["CE20215057"],"award-info":[{"award-number":["CE20215057"]}]},{"name":"major project of Basic science (Natural science) research in colleges and universities of Jiangsu Province","award":["CZ20220030"],"award-info":[{"award-number":["CZ20220030"]}]},{"name":"major project of Basic science (Natural science) research in colleges and universities of Jiangsu Province","award":["CQ20220092"],"award-info":[{"award-number":["CQ20220092"]}]},{"name":"major project of Basic science (Natural science) research in colleges and universities of Jiangsu Province","award":["22KJA580001"],"award-info":[{"award-number":["22KJA580001"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Numerical solutions and approximate solutions of fractional differential equations have been studied by mathematicians recently and approximate solutions and exact solutions of fractional differential equations are obtained in many kinds of ways, such as Lie symmetry, variational method, the optimal ADM method, and so on. In this paper, we obtain the positive solutions by iterative methods for sum operators. Green\u2019s function and the properties of Green\u2019s function are deduced, then based on the properties of Green\u2019s function, the existence of iterative positive solutions for a nonlinear Caputo\u2013Hadamard infinite-point fractional differential equation are obtained by iterative methods for sum operators; an example is proved to illustrate the main result.<\/jats:p>","DOI":"10.3390\/sym15050970","type":"journal-article","created":{"date-parts":[[2023,4,24]],"date-time":"2023-04-24T06:20:42Z","timestamp":1682317242000},"page":"970","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Existence of Monotone Positive Solutions for Caputo\u2013Hadamard Nonlinear Fractional Differential Equation with Infinite-Point Boundary Value Conditions"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4779-4181","authenticated-orcid":false,"given":"Limin","family":"Guo","sequence":"first","affiliation":[{"name":"School of Automotive Engineering, Changzhou Institute of Technology, Changzhou 213002, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1018-0087","authenticated-orcid":false,"given":"Cheng","family":"Li","sequence":"additional","affiliation":[{"name":"School of Automotive Engineering, Changzhou Institute of Technology, Changzhou 213002, China"}]},{"given":"Jingbo","family":"Zhao","sequence":"additional","affiliation":[{"name":"School of Automotive Engineering, Changzhou Institute of Technology, Changzhou 213002, China"}]}],"member":"1968","published-online":{"date-parts":[[2023,4,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.vlsi.2021.11.002","article-title":"Neural network adaptive control for a class of uncertain fractional order nonlinear systems","volume":"83","author":"Boulham","year":"2022","journal-title":"Integration"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"3921","DOI":"10.1016\/j.aej.2021.02.054","article-title":"A fractional order viscoelastic-plastic creep model for coal sample considering initial damage accumulation","volume":"60","author":"Huang","year":"2021","journal-title":"Alex. 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