{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,15]],"date-time":"2026-04-15T19:13:35Z","timestamp":1776280415438,"version":"3.50.1"},"reference-count":37,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2022,12,20]],"date-time":"2022-12-20T00:00:00Z","timestamp":1671494400000},"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>We propose a solution to the symmetric nonlinear \u03a8-Caputo fractional integro differential equations involving non-instantaneous impulsive boundary conditions. We investigate the existence and uniqueness of the solution for the proposed problem. Banach contraction theorem is employed to prove the uniqueness results, while Krasnoselkii\u2019s fixed point technique is used to prove the existence results. Additionally, an example is used to explain the results. In this manner, our results represent generalized versions of some recent interesting contributions.<\/jats:p>","DOI":"10.3390\/sym15010005","type":"journal-article","created":{"date-parts":[[2022,12,21]],"date-time":"2022-12-21T02:58:27Z","timestamp":1671591507000},"page":"5","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["On Nonlinear \u03a8-Caputo Fractional Integro Differential Equations Involving Non-Instantaneous Conditions"],"prefix":"10.3390","volume":"15","author":[{"given":"Ramasamy","family":"Arul","sequence":"first","affiliation":[{"name":"Department of Mathematics, Gnanamani College of Technology, Namakkal 637018, Tamil Nadu, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Panjayan","family":"Karthikeyan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Sri Vasavi College, Erode 638316, Tamil Nadu, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4138-7067","authenticated-orcid":false,"given":"Kulandhaivel","family":"Karthikeyan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, KPR Institute of Engineering and Technology, Coimbatore 641407, Tamil Nadu, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Palanisamy","family":"Geetha","sequence":"additional","affiliation":[{"name":"Department of Mathematics, KPR Institute of Engineering and Technology, Coimbatore 641407, Tamil Nadu, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6562-9705","authenticated-orcid":false,"given":"Ymnah","family":"Alruwaily","sequence":"additional","affiliation":[{"name":"Mathematics Department, College of Science, Jouf University, P.O. Box 2014, Sakaka 72388, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lamya","family":"Almaghamsi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, University of Jeddah, P.O. Box 80327, Jeddah 21589, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4955-0842","authenticated-orcid":false,"given":"El-sayed","family":"El-hady","sequence":"additional","affiliation":[{"name":"Mathematics Department, College of Science, Jouf University, P.O. Box 2014, Sakaka 72388, Saudi Arabia"},{"name":"Basic Science Department, Faculty of Computers and Informatics, Suez Canal University, Ismailia 41522, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,12,20]]},"reference":[{"key":"ref_1","unstructured":"Podlubny, I. (1999). 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