{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,12]],"date-time":"2025-12-12T13:09:53Z","timestamp":1765544993587,"version":"build-2065373602"},"reference-count":19,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2025,1,22]],"date-time":"2025-01-22T00:00:00Z","timestamp":1737504000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004775","name":"Natural Science Foundation of Gansu Province","doi-asserted-by":"publisher","award":["24JRRA994"],"award-info":[{"award-number":["24JRRA994"]}],"id":[{"id":"10.13039\/501100004775","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Northwest Minzu University","award":["24JRRA994"],"award-info":[{"award-number":["24JRRA994"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>The regularized \u03c8-Hilfer derivative within the sense of Caputo is an improved version of the \u03c8-Hilfer fractional derivative, primarily because it addresses the issue where the initial conditions of problems involving the \u03c8-Hilfer fractional derivative lack clear physical significance unless p=1. This article\u2019s main contribution is the use of the \u03c8-Laplace transform, which is the first to provide an explicit expression for mild solutions to the fractional diffusion equations with the regularized \u03c8-Hilfer derivative. Additionally, we investigate the existence and attractivity of mild solutions for fractional diffusion equations involving the regularized \u03c8-Hilfer fractional derivatives. Finally, we provide two examples to illustrate our main results.<\/jats:p>","DOI":"10.3390\/axioms14020079","type":"journal-article","created":{"date-parts":[[2025,1,22]],"date-time":"2025-01-22T09:52:20Z","timestamp":1737539540000},"page":"79","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Existence and Attractivity of Mild Solutions for Fractional Diffusion Equations Involving the Regularized \u03c8-Hilfer Fractional Derivatives"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0009-0001-3940-0146","authenticated-orcid":false,"given":"Luyao","family":"Wang","sequence":"first","affiliation":[{"name":"School of Mathematics and Computer Science, Northwest Minzu University, Lanzhou 730030, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0001-3784-0316","authenticated-orcid":false,"given":"Yuhang","family":"Jin","sequence":"additional","affiliation":[{"name":"School of Mathematics and Computer Science, Northwest Minzu University, Lanzhou 730030, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0005-6990-4790","authenticated-orcid":false,"given":"Wenchang","family":"He","sequence":"additional","affiliation":[{"name":"School of Mathematics and Computer Science, Northwest Minzu University, Lanzhou 730030, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6176-5950","authenticated-orcid":false,"given":"Jia","family":"Mu","sequence":"additional","affiliation":[{"name":"School of Mathematics and Computer Science, Northwest Minzu University, Lanzhou 730030, China"},{"name":"Key Laboratory of Streaming Data Computing Technologies and Application, Northwest Minzu University, Lanzhou 730030, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,1,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2921","DOI":"10.1016\/j.aej.2020.03.027","article-title":"Fractional diffusion equation with new fractional operator","volume":"59","author":"Sene","year":"2020","journal-title":"Alex. 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