{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:26:07Z","timestamp":1760059567860,"version":"build-2065373602"},"reference-count":20,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2025,6,22]],"date-time":"2025-06-22T00:00:00Z","timestamp":1750550400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Naresuan University, Thailand","award":["R2568E016"],"award-info":[{"award-number":["R2568E016"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This paper establishes the well-posedness of Cauchy-type problems with non-symmetric initial conditions for nonlinear implicit Hilfer fractional differential equations of general fractional orders in weighted function spaces. Using fixed-point techniques, we first prove the existence of solutions via Schaefer\u2019s fixed-point theorem. The uniqueness and Ulam\u2013Hyers stability are then derived using Banach\u2019s contraction principle. By introducing a novel singular-kernel Gronwall inequality, we extend the analysis to Ulam\u2013Hyers\u2013Rassias stability and continuous dependence on initial data. The theoretical framework is unified for general fractional orders and validated through examples, demonstrating its applicability to implicit systems with memory effects. Key contributions include weighted-space analysis and stability criteria for this class of equations.<\/jats:p>","DOI":"10.3390\/sym17070986","type":"journal-article","created":{"date-parts":[[2025,6,24]],"date-time":"2025-06-24T10:44:41Z","timestamp":1750761881000},"page":"986","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Well-Posedness of Cauchy-Type Problems for Nonlinear Implicit Hilfer Fractional Differential Equations with General Order in Weighted Spaces"],"prefix":"10.3390","volume":"17","author":[{"given":"Jakgrit","family":"Sompong","sequence":"first","affiliation":[{"name":"Department of Mathematics, Naresuan University, Phitsanulok 65000, Thailand"}]},{"given":"Samten","family":"Choden","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Naresuan University, Phitsanulok 65000, Thailand"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2459-3261","authenticated-orcid":false,"given":"Ekkarath","family":"Thailert","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Naresuan University, Phitsanulok 65000, Thailand"},{"name":"Research Center for Academic Excellence in Mathematics, Naresuan University, Phitsanulok 65000, Thailand"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7695-2118","authenticated-orcid":false,"given":"Sotiris K.","family":"Ntouyas","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece"}]}],"member":"1968","published-online":{"date-parts":[[2025,6,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Diethelm, K. (2010). The Analysis of Fractional Differential Equations, Springer.","DOI":"10.1007\/978-3-642-14574-2"},{"key":"ref_2","unstructured":"Kilbas, A.A., Srivastava, H.M., and Trujillo, J.J. (2006). Theory and Applications of Fractional Differential Equations, Elsevier."},{"key":"ref_3","unstructured":"Miller, K.S., and Ross, B. (1993). An Introduction to the Fractional Calculus and Fractional Differential Equations, Wiley."},{"key":"ref_4","unstructured":"Podlubny, I. (1999). Fractional Differential Equations, Academic Press."},{"key":"ref_5","unstructured":"Samko, S.G., Kilbas, A.A., and Marichev, O.I. (1993). Fractional Integrals and Derivatives: Theory and Applications, Gordon and Breach."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Telli, B., Souid, M.S., Alzabut, J., and Khan, H. (2023). Existence and uniqueness theorems for a variable-order fractional differential equation with delay. 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Anal."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/7\/986\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T17:56:36Z","timestamp":1760032596000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/7\/986"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,6,22]]},"references-count":20,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2025,7]]}},"alternative-id":["sym17070986"],"URL":"https:\/\/doi.org\/10.3390\/sym17070986","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2025,6,22]]}}}