{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:10:12Z","timestamp":1760242212399,"version":"build-2065373602"},"reference-count":43,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2017,1,24]],"date-time":"2017-01-24T00:00:00Z","timestamp":1485216000000},"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>In this paper, we study the existence of homoclinic solutions for the fractional Hamiltonian systems with left and right Liouville\u2013Weyl derivatives. We establish some new results concerning the existence and multiplicity of homoclinic solutions for the given system by using Clark\u2019s theorem from critical point theory and fountain theorem.<\/jats:p>","DOI":"10.3390\/e19020050","type":"journal-article","created":{"date-parts":[[2017,1,24]],"date-time":"2017-01-24T10:20:29Z","timestamp":1485253229000},"page":"50","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Multiplicity of Homoclinic Solutions for Fractional Hamiltonian Systems with Subquadratic Potential"],"prefix":"10.3390","volume":"19","author":[{"given":"Neamat","family":"Nyamoradi","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Sciences, Razi University, Kermanshah 67149, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3452-8922","authenticated-orcid":false,"given":"Ahmed","family":"Alsaedi","sequence":"additional","affiliation":[{"name":"Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5350-2977","authenticated-orcid":false,"given":"Bashir","family":"Ahmad","sequence":"additional","affiliation":[{"name":"Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yong","family":"Zhou","sequence":"additional","affiliation":[{"name":"Faculty of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, China"},{"name":"Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2017,1,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"128","DOI":"10.1007\/BF02742713","article-title":"Les M\u00e9thodes Nouvelles de la M\u00e9canique C\u00e9leste","volume":"10","author":"Magini","year":"1899","journal-title":"Il Nuovo Cimento"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1007\/BF01444526","article-title":"A variational approach to homoclinic orbits in Hamiltonian systems","volume":"288","author":"Zelati","year":"1990","journal-title":"Math. 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