{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,17]],"date-time":"2026-06-17T20:15:58Z","timestamp":1781727358530,"version":"3.54.5"},"reference-count":40,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2024,2,19]],"date-time":"2024-02-19T00:00:00Z","timestamp":1708300800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Deanship of Scientific Research, Vice Presidency for Graduate Studies and Scientific Research, King Faisal University, Saudi Arabia","award":["GRANT5830"],"award-info":[{"award-number":["GRANT5830"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This paper focuses on studying the uniqueness of the mild solution for an abstract fractional differential equation. We use Banach\u2019s fixed point theorem to prove this uniqueness. Additionally, we examine the stability properties of the equation using Ulam\u2019s stability. To analyze these properties, we consider the involvement of Hadamard fractional derivatives. Throughout this study, we put significant emphasis on the role and properties of resolvent operators. Furthermore, we investigate Ulam-type stability by providing examples of partial fractional differential equations that incorporate Hadamard derivatives.<\/jats:p>","DOI":"10.3390\/axioms13020131","type":"journal-article","created":{"date-parts":[[2024,2,19]],"date-time":"2024-02-19T04:39:36Z","timestamp":1708317576000},"page":"131","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Study of Uniqueness and Ulam-Type Stability of Abstract Hadamard Fractional Differential Equations of Sobolev Type via Resolvent Operators"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0009-0004-3759-2211","authenticated-orcid":false,"given":"Khellaf","family":"Ould Melha","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Exact Sciences and Informatics, Hassiba Benbouali University, Ouled Fares 02180, Chlef, Algeria"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0413-5626","authenticated-orcid":false,"given":"Abdelhamid","family":"Mohammed Djaouti","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Sciences, King Faisal University, Hofuf 31982, Al-Ahsa, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2349-3445","authenticated-orcid":false,"given":"Muhammad Amer","family":"Latif","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Sciences, King Faisal University, Hofuf 31982, Al-Ahsa, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4246-8405","authenticated-orcid":false,"given":"Vaijanath L.","family":"Chinchane","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Deogiri Institute of Engineering and Management Studies, Chhatrapati, Sambhajinagar 431005, India"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2024,2,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Hilfer, R. 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