{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,2]],"date-time":"2026-01-02T17:29:50Z","timestamp":1767374990748,"version":"build-2065373602"},"reference-count":20,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2021,3,8]],"date-time":"2021-03-08T00:00:00Z","timestamp":1615161600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Fractal Fract"],"abstract":"<jats:p>In this work, we investigate a class of nonlocal integro-differential equations involving Hilfer fractional derivatives and almost sectorial operators. We prove our results by applying Schauder\u2019s fixed point technique. Moreover, we show the fundamental properties of the representation of the solution by discussing two cases related to the associated semigroup. For that, we consider compactness and noncompactness properties, respectively. Furthermore, an example is given to illustrate the obtained theory.<\/jats:p>","DOI":"10.3390\/fractalfract5010022","type":"journal-article","created":{"date-parts":[[2021,3,8]],"date-time":"2021-03-08T23:04:39Z","timestamp":1615244679000},"page":"22","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":35,"title":["Analysis of Hilfer Fractional Integro-Differential Equations with Almost Sectorial Operators"],"prefix":"10.3390","volume":"5","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4138-7067","authenticated-orcid":false,"given":"Kulandhaivel","family":"Karthikeyan","sequence":"first","affiliation":[{"name":"Department of Mathematics, Centre for Research and Development, KPR Institute of Engineering and Technology, Coimbatore, Tamil Nadu 641407, India"}]},{"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"},{"name":"Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8641-2505","authenticated-orcid":false,"given":"Delfim F. 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