{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,29]],"date-time":"2026-01-29T13:22:15Z","timestamp":1769692935156,"version":"3.49.0"},"reference-count":30,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2023,6,2]],"date-time":"2023-06-02T00:00:00Z","timestamp":1685664000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, we introduce a novel form of interpolative convex contraction and develop some new theorems by utilizing the progressive method of interpolative convex contractions. We also obtain some fixed point results for a Suzuki convex contraction in orbitally S-complete F-metric spaces. The second purpose of this research is to evaluate the effectiveness of the fixed point approach in solving fractional differential equations with boundary conditions.<\/jats:p>","DOI":"10.3390\/sym15061189","type":"journal-article","created":{"date-parts":[[2023,6,2]],"date-time":"2023-06-02T08:50:31Z","timestamp":1685695831000},"page":"1189","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Fractional Differential Boundary Value Equation Utilizing the Convex Interpolation for Symmetry of Variables"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7742-5993","authenticated-orcid":false,"given":"Aftab","family":"Hussain","sequence":"first","affiliation":[{"name":"Department of Mathematics, King Abdulaziz University, P.O. 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Existence theorems for (\u03c8,\u03d5)-orthogonal interpolative contractions and an application to fractional differential equations. Optimization.","DOI":"10.1080\/02331934.2022.2043858"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"6461477","DOI":"10.1155\/2021\/6461477","article-title":"Generalized Interpolative Contractions and an Application","volume":"2021","author":"Nazam","year":"2021","journal-title":"J. Math."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"845","DOI":"10.1515\/math-2022-0042","article-title":"Remarks on the generalized interpolative contractions and some fixed-point theorems with application","volume":"20","author":"Nazam","year":"2022","journal-title":"Open Math."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"128","DOI":"10.1007\/s11784-018-0606-6","article-title":"On a new generalization of metric spaces","volume":"20","author":"Jleli","year":"2018","journal-title":"J. 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Math."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"793486","DOI":"10.1155\/2012\/793486","article-title":"Generalized (\u03b1-\u03c8) contractive type mappings and related fixed point theorems with applications","volume":"2012","author":"Karapinar","year":"2012","journal-title":"Abstr. Appl. Anal."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"657858","DOI":"10.1155\/2014\/657858","article-title":"On Modified \u03b1-\u03b7-Contractive mappings","volume":"2014","author":"Kutbi","year":"2014","journal-title":"Abstr. Appl. Anal."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Hammad, H.A., Agarwal, R.P., Momani, S., and Alsharari, F. (2021). Solving a Fractional-Order Differential Equation Using Rational Symmetric Contraction Mappings. Fractal Fract., 5.","DOI":"10.3390\/fractalfract5040159"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"280817","DOI":"10.1155\/2014\/280817","article-title":"Fixed Point Theory in \u03b1-Complete Metric Spaces with Applications","volume":"2014","author":"Hussain","year":"2014","journal-title":"Abstr. Appl. Anal."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"158","DOI":"10.1186\/s13663-015-0407-1","article-title":"Fixed point results for generalized F-contractions in modular metric and fuzzy metric spaces","volume":"2015","author":"Hussain","year":"2015","journal-title":"Fixed Point Theory Appl."},{"key":"ref_23","first-page":"8","article-title":"Some existence results for a nonlinear fractional differential equation on partially ordered Banach spaces","volume":"112","author":"Baleanu","year":"2013","journal-title":"Bound. Value Probl."},{"key":"ref_24","first-page":"1465623","article-title":"Solvability of Some Two-Point Fractional Boundary Value Problems under Barrier Strip Conditions","volume":"2017","author":"He","year":"2017","journal-title":"J. Funct. Spaces."},{"key":"ref_25","unstructured":"Miller, K.S., and Ross, B. (1993). An Introduction to the Fractional Calculus and Fractional Differential Eqautions, John Wiley & Sons."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1016\/j.jmaa.2011.05.082","article-title":"Impulsive periodic boundary value problems for fractional differential equation involving Riemann-Liouville sequential fractional derivative","volume":"384","author":"Bai","year":"2011","journal-title":"J. Math. Anal. Appl."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Tudorache, A., and Luca, R. (2023). On a System of Sequential Caputo Fractional Differential Equations with Nonlocal Boundary Conditions. Fractal Fract., 7.","DOI":"10.3390\/fractalfract7020181"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"7093","DOI":"10.3934\/math.2022395","article-title":"Involvement of the fixed point technique for solving a fractional differential system","volume":"7","author":"Hammad","year":"2022","journal-title":"AIMS Math."},{"key":"ref_29","unstructured":"Kilbas, A.A., Srivastava, H.M., and Trujillo, J.J. (2006). Theory and Applications of Fractional Differential Equations, North-Holland Mathematics Sudies Elsevier Sci. B.V."},{"key":"ref_30","first-page":"709","article-title":"Generalized fractional derivatives and Laplace transform","volume":"13","author":"Jarad","year":"2020","journal-title":"Discret. Contin. Dyn. 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