{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,26]],"date-time":"2026-06-26T14:40:45Z","timestamp":1782484845205,"version":"3.54.5"},"reference-count":35,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2021,11,3]],"date-time":"2021-11-03T00:00:00Z","timestamp":1635897600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The goal of this paper is to consider a new class of \u03c6-Hilfer fractional differential equations with impulses and nonlocal conditions. By using fractional calculus, semigroup theory, and with the help of the fixed point theorem, the existence and uniqueness of mild solutions are obtained for the proposed fractional system. Symmetrically, we discuss the existence of optimal controls for the \u03c6-Hilfer fractional control system. Our main results are well supported by an illustrative example.<\/jats:p>","DOI":"10.3390\/sym13112084","type":"journal-article","created":{"date-parts":[[2021,11,3]],"date-time":"2021-11-03T21:57:49Z","timestamp":1635976669000},"page":"2084","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":19,"title":["Analysis and Optimal Control of \u03c6-Hilfer Fractional Semilinear Equations Involving Nonlocal Impulsive Conditions"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8406-7071","authenticated-orcid":false,"given":"Sarra","family":"Guechi","sequence":"first","affiliation":[{"name":"Department of Mathematics, Guelma University, Guelma 24000, Algeria"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6946-8400","authenticated-orcid":false,"given":"Rajesh","family":"Dhayal","sequence":"additional","affiliation":[{"name":"School of Mathematics, Thapar Institute of Engineering and Technology, Patiala 147 004, India"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4321-9515","authenticated-orcid":false,"given":"Amar","family":"Debbouche","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Guelma University, Guelma 24000, Algeria"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0055-7581","authenticated-orcid":false,"given":"Muslim","family":"Malik","sequence":"additional","affiliation":[{"name":"School of Basic Sciences, Indian Institute of Technology Mandi, Kamand 175 005, India"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2021,11,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Zhou, Y., Wang, J., and Zhang, L. 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