{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:34:37Z","timestamp":1760060077898,"version":"build-2065373602"},"reference-count":17,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2025,7,31]],"date-time":"2025-07-31T00:00:00Z","timestamp":1753920000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this work, we study Caputo fractional boundary value problems and contribute to the theory of fractional differential equations by improving the results of Ferreira. Specifically, we establish sharper bounds for the Green\u2019s functions associated with the problems and apply Rus\u2019s fixed-point theorem. Our results hold under a less restrictive assumption, thereby extending the class of problems for which the existence and uniqueness of solutions can be ensured. This is demonstrated through numerical validation presented in the final stage of our analysis. An important aspect of this approach is that it avoids the need for strong contraction conditions, suggesting potential applicability to a broader range of differential equations.<\/jats:p>","DOI":"10.3390\/axioms14080592","type":"journal-article","created":{"date-parts":[[2025,8,5]],"date-time":"2025-08-05T08:46:55Z","timestamp":1754383615000},"page":"592","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Enhanced Qualitative Understanding of Solutions to Fractional Boundary Value Problems via Alternative Fixed-Point Methods"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9399-3253","authenticated-orcid":false,"given":"Saleh S.","family":"Almuthaybiri","sequence":"first","affiliation":[{"name":"Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1305-4959","authenticated-orcid":false,"given":"Abdelhamid","family":"Zaidi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia"}]},{"given":"Christopher C.","family":"Tisdell","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, The University of New South Wales (UNSW), Sydney, NSW 2052, Australia"}]}],"member":"1968","published-online":{"date-parts":[[2025,7,31]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1016\/j.aml.2016.10.008","article-title":"Sharp estimates for the unique solution of two-point fractional-order boundary value problems","volume":"65","author":"Ahmad","year":"2017","journal-title":"Appl. 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Anal."},{"key":"ref_9","unstructured":"Kilbas, A.A., Srivastava, H.M., and Trujillo, J.J. (2006). Theory and Applications of Fractional Differential Equations, Volume 204 (North-Holland Mathematics Studies), Elsevier."},{"key":"ref_10","unstructured":"Samko, S.G., Kilbas, A.A., and Marichev, O.I. (1993). Fractional Integrals and Derivatives, Springer."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"5731","DOI":"10.3934\/math.2025264","article-title":"Explicit evaluations of subfamilies of the hypergeometric function 3F2(1) along with specific fractional integrals","volume":"10","author":"Zaidi","year":"2025","journal-title":"AIMS Math."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Sohrab, H.H. (2014). Basic Real Analysis, Birkh\u00e4user\/Springer. [2nd ed.].","DOI":"10.1007\/978-1-4939-1841-6"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Bernstein, D.S. (2009). Matrix Mathematics, Princeton University Press. [2nd ed.]. 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