{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:31:32Z","timestamp":1760149892993,"version":"build-2065373602"},"reference-count":29,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2023,9,8]],"date-time":"2023-09-08T00:00:00Z","timestamp":1694131200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"King Saud University, Riyadh, Saudi Arabia","award":["RSPD2023R974"],"award-info":[{"award-number":["RSPD2023R974"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This paper explores the realm of fractional integral calculus in connection with the one-dimensional Dunkl operator on the space of tempered functions and Lizorkin type space. The primary objective is to construct fractional integral operators within this framework. By establishing the analogous counterparts of well-known operators, including the Riesz fractional integral, Feller fractional integral, and Riemann\u2013Liouville fractional integral operators, we demonstrate their applicability in this setting. Moreover, we show that familiar properties of fractional integrals can be derived from the obtained results, further reinforcing their significance. This investigation sheds light on the utilization of Dunkl operators in fractional calculus and provides valuable insights into the connections between different types of fractional integrals. The findings presented in this paper contribute to the broader field of fractional calculus and advance our understanding of the study of Dunkl operators in this context.<\/jats:p>","DOI":"10.3390\/sym15091725","type":"journal-article","created":{"date-parts":[[2023,9,8]],"date-time":"2023-09-08T07:52:11Z","timestamp":1694159531000},"page":"1725","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Fractional Integrals Associated with the One-Dimensional Dunkl Operator in Generalized Lizorkin Space"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2743-2036","authenticated-orcid":false,"given":"Fethi","family":"Bouzeffour","sequence":"first","affiliation":[{"name":"Department of Mathematics, College of Sciences, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,9,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1090\/conm\/138\/1199124","article-title":"Hankel transforms associated to finite reflections groups","volume":"138","author":"Dunkl","year":"1992","journal-title":"Contemp. Math."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1090\/S0002-9947-1989-0951883-8","article-title":"Differential-difference operators associated with reflections groups","volume":"311","author":"Dunkl","year":"1989","journal-title":"Trans. Amer. Math. Soc."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1080\/10652460212888","article-title":"Paley-Wiener Theorems for the Dunkl transform and Dunkl translation operators","volume":"13","year":"2002","journal-title":"Integral Transform. Spec. 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