{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,21]],"date-time":"2026-02-21T12:31:03Z","timestamp":1771677063766,"version":"3.50.1"},"reference-count":18,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2025,3,12]],"date-time":"2025-03-12T00:00:00Z","timestamp":1741737600000},"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>The stability analysis of Timoshenko beam systems that incorporate delays and fractional boundary controls is a complex area of study in the field of viscoelasticity. Our study aims to balance the symmetric influence of internal viscoelastic damping and boundary fractional damping in a structured way. The goal is to establish a system where both effects contribute symmetrically to the overall stability and dynamics. In this paper, we study the stability of certain hyperbolic evolution problems, in particular, a Timoshenko system in viscoelasticity with fractional time delay and fractional boundary controls. We prove, under assumptions on the data, the lack of exponential stability decay rate when \u03b7\u22650 and polynomial stability decay rate when \u03b7&gt;0 using energy methods.<\/jats:p>","DOI":"10.3390\/sym17030423","type":"journal-article","created":{"date-parts":[[2025,3,12]],"date-time":"2025-03-12T04:55:44Z","timestamp":1741755344000},"page":"423","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Loss of Exponential Stability for a Delayed Timoshenko System Symmetrically in Both Viscoelasticity and Fractional Boundary Controls"],"prefix":"10.3390","volume":"17","author":[{"given":"Mokhtaria Bouariba","family":"Sadoun","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Abou Bekr Belkaid, Tlemcen 13000, Algeria"}]},{"given":"Amine Benaissa","family":"Cherif","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Sciences and Technology Oran Mohamed Boudiaf, Oran 31000, Algeria"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3177-663X","authenticated-orcid":false,"given":"Rachid","family":"Bentifour","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Abou Bekr Belkaid, Tlemcen 13000, Algeria"}]},{"given":"Keltoum","family":"Bouhali","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, Qassim University, P.O. Box 6644, Buraydah 51452, Saudi Arabia"}]},{"given":"Mohamed","family":"Biomy","sequence":"additional","affiliation":[{"name":"Department of Management Information Systems, College of Business Administration, Qassim University, Buraydah 52571, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7895-4168","authenticated-orcid":false,"given":"Khaled","family":"Zennir","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, Qassim University, P.O. Box 6644, Buraydah 51452, Saudi Arabia"}]}],"member":"1968","published-online":{"date-parts":[[2025,3,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1068","DOI":"10.1016\/j.jmaa.2007.11.012","article-title":"Timoshenko systems with indefinite damping","volume":"341","author":"Racke","year":"2008","journal-title":"J. Math. Anal. 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Equ."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"126520","DOI":"10.1016\/j.jmaa.2022.126520","article-title":"Viscoelastic Timoshenko beams with variable-exponent nonlinearity","volume":"516","author":"Mustafa","year":"2022","journal-title":"J. Math. Anal. Appl."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"4","DOI":"10.1007\/s40314-019-0982-6","article-title":"Discrete energy behavior of a damped Timoshenko system","volume":"39","author":"Sabrine","year":"2020","journal-title":"Comp. Appl. Math."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"2692","DOI":"10.1080\/00036811.2022.2033233","article-title":"Stability of a viscoelastic Timoshenko system with non-monotonic kernel","volume":"102","author":"Zhang","year":"2022","journal-title":"Appl. Anal."},{"key":"ref_8","first-page":"34","article-title":"Free Vibrations of Two-Span Timoshenko Beams with Adjoint Oscillator","volume":"4","author":"Mizhidon","year":"2013","journal-title":"Syst. Anal. Model."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Braik, A., Mirgani, S.M., Hassan, E.I., and Zennir, K. (2023). Well-Posedness and Energy Decay Rates for a Timoshenko-Type System with Internal Time-Varying Delay in the Displacement. Symmetry, 15.","DOI":"10.3390\/sym15101878"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"385","DOI":"10.1007\/s12046-008-0026-1","article-title":"Free Vibrations of a Multi-Span Timoshenko Beam Carrying Multiple Spring-Mass Systems","volume":"33","author":"Yesilce","year":"2008","journal-title":"Sadhana"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"385","DOI":"10.1007\/s40324-021-00239-0","article-title":"Well-posedness and energy decay for some thermoelastic systems of Timoshenko type with Kelvin\u2013Voigt damping","volume":"78","author":"Dridi","year":"2021","journal-title":"SeMA J."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"2945","DOI":"10.1016\/S0020-7683(96)00217-X","article-title":"Nonlinear vibrations of Timoshenko pipes conveying fluid","volume":"34","author":"Lin","year":"1997","journal-title":"Int. J. 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Anal."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/3\/423\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T16:51:04Z","timestamp":1760028664000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/3\/423"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,3,12]]},"references-count":18,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2025,3]]}},"alternative-id":["sym17030423"],"URL":"https:\/\/doi.org\/10.3390\/sym17030423","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,3,12]]}}}