{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,19]],"date-time":"2026-03-19T06:29:32Z","timestamp":1773901772428,"version":"3.50.1"},"reference-count":15,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2021,10,8]],"date-time":"2021-10-08T00:00:00Z","timestamp":1633651200000},"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>In this manuscript, we establish the existence of results of fractional impulsive differential equations involving \u03c8-Hilfer fractional derivative and almost sectorial operators using Schauder fixed-point theorem. We discuss two cases, if the associated semigroup is compact and noncompact, respectively. We consider here the higher-dimensional system of integral equations. We present herewith new theoretical results, structural investigations, and new models and approaches. Some special cases of the results are discussed as well. Due to the nature of measurement of noncompactness theory, there exists a strong relationship between the sectorial operator and symmetry. When working on either of the concepts, it can be applied to the other one as well. Finally, a case study is presented to demonstrate the major theory.<\/jats:p>","DOI":"10.3390\/sym13101895","type":"journal-article","created":{"date-parts":[[2021,10,11]],"date-time":"2021-10-11T01:59:47Z","timestamp":1633917587000},"page":"1895","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["Analysis on \u03c8-Hilfer Fractional Impulsive Differential Equations"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4138-7067","authenticated-orcid":false,"given":"Kulandhaivel","family":"Karthikeyan","sequence":"first","affiliation":[{"name":"Department of Mathematics, KPR Institute of Engineering and Technology, Coimbatore 641 407, Tamil Nadu, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6712-9819","authenticated-orcid":false,"given":"Panjaiyan","family":"Karthikeyan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Sri Vasavi College, Erode 638 316, Tamil Nadu, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6146-5544","authenticated-orcid":false,"given":"Dimplekumar N.","family":"Chalishajar","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, Virginia Military Institute, 435 Mallory Hall, Lexington, VA 24450, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7129-8180","authenticated-orcid":false,"given":"Duraisamy Senthil","family":"Raja","sequence":"additional","affiliation":[{"name":"Department of Mathematics, K.S.Rangasamy College of Technology, Tiruchengode 637 215, Tamil Nadu, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4227-9519","authenticated-orcid":false,"given":"Ponnusamy","family":"Sundararajan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Arinagar Anna Government Arts College, Namakkal 637 002, Tamil Nadu, India"}]}],"member":"1968","published-online":{"date-parts":[[2021,10,8]]},"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","first-page":"399","DOI":"10.1016\/S0301-0104(02)00670-5","article-title":"Experimental evidence for fractional time evolution in glass forming materials","volume":"284","author":"Hilfer","year":"2002","journal-title":"Chem. Phys."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"226","DOI":"10.1186\/s13662-018-1679-7","article-title":"Impulsive Hilfer fractional derivative differential equations","volume":"2018","author":"Ahmed","year":"2018","journal-title":"Adv. Differ. Equ."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1016\/j.cam.2016.05.014","article-title":"A new representation formula for the Hilfer fractional derivative and its application","volume":"308","author":"Kamocki","year":"2016","journal-title":"J. Comput. Appl. 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Basic Theory of Fractional Differential Equations, World Scientific.","DOI":"10.1142\/9069"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/10\/1895\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T07:10:31Z","timestamp":1760166631000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/10\/1895"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,10,8]]},"references-count":15,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2021,10]]}},"alternative-id":["sym13101895"],"URL":"https:\/\/doi.org\/10.3390\/sym13101895","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,10,8]]}}}