{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,23]],"date-time":"2026-03-23T15:51:34Z","timestamp":1774281094454,"version":"3.50.1"},"reference-count":16,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2016,11,23]],"date-time":"2016-11-23T00:00:00Z","timestamp":1479859200000},"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 manuscript, we prove the existence and uniqueness of solutions for local fractional differential equations (LFDEs) with local fractional derivative operators (LFDOs). By using the contracting mapping theorem (CMT) and increasing and decreasing theorem (IDT), existence and uniqueness results are obtained. Some examples are presented to illustrate the validity of our results.<\/jats:p>","DOI":"10.3390\/e18110420","type":"journal-article","created":{"date-parts":[[2016,11,23]],"date-time":"2016-11-23T11:12:14Z","timestamp":1479899534000},"page":"420","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":26,"title":["On the Existence and Uniqueness of Solutions for Local Fractional Differential Equations"],"prefix":"10.3390","volume":"18","author":[{"given":"Hossein","family":"Jafari","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar 47416, Iran"},{"name":"Department of Mathematical Sciences, University of South Africa (UNISA), Pretoria 0003, South Africa"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hassan","family":"Jassim","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Education for Pure Sciences, University of Thi-Qar, Nasiriyah 64001, Iraq"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0979-5746","authenticated-orcid":false,"given":"Maysaa","family":"Al Qurashi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, King Saud University, P.O. Box 22452, Riyadh 11495, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0286-7244","authenticated-orcid":false,"given":"Dumitru","family":"Baleanu","sequence":"additional","affiliation":[{"name":"Department of Mathematics, \u00c7ankaya University, Ankara 06530, Turkey"},{"name":"Institute of Space Sciences, P.O. Box MG-23, Magurele-Bucharest RO-76911, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2016,11,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Hilfer, R. (2000). Applications of Fractional Calculus in Physics, World Scientific.","DOI":"10.1142\/9789812817747"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Agarwal, R.B., Meehan, M., and Regan, D. (2001). 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