{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,5]],"date-time":"2026-02-05T11:41:43Z","timestamp":1770291703990,"version":"3.49.0"},"reference-count":36,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2020,7,10]],"date-time":"2020-07-10T00:00:00Z","timestamp":1594339200000},"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 telegraph model describes that the current and voltage waves can be reflected on a wire, that symmetrical wave patterns can form along a line. A numerical study of these voltage and current waves on a transferral line has been proposed via a modified extended cubic B-spline (MECBS) method. The B-spline functions have the flexibility and high order accuracy to approximate the solutions. These functions also preserve the symmetrical property. The MECBS and Crank Nicolson technique are employed to find out the solution of the non-linear time fractional telegraph equation. The time direction is discretized in the Caputo sense while the space dimension is discretized by the modified extended cubic B-spline. The non-linearity in the equation is linearized by Taylor\u2019s series. The proposed algorithm is unconditionally stable and convergent. The numerical examples are displayed to verify the authenticity and implementation of the method.<\/jats:p>","DOI":"10.3390\/sym12071154","type":"journal-article","created":{"date-parts":[[2020,7,10]],"date-time":"2020-07-10T09:45:31Z","timestamp":1594374331000},"page":"1154","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":38,"title":["Novel Numerical Approach Based on Modified Extended Cubic B-Spline Functions for Solving Non-Linear Time-Fractional Telegraph Equation"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1825-2631","authenticated-orcid":false,"given":"Tayyaba","family":"Akram","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences, Universiti Sains Malaysia, Penang 11800, Malaysia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0491-1528","authenticated-orcid":false,"given":"Muhammad","family":"Abbas","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5103-6092","authenticated-orcid":false,"given":"Azhar","family":"Iqbal","sequence":"additional","affiliation":[{"name":"Mathematics and Natural Sciences, Prince Mohammad Bin Fahd University, Al Khobar 31952, Saudia Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0286-7244","authenticated-orcid":false,"given":"Dumitru","family":"Baleanu","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Arts and Sciences, Cankaya University, Ankara 06530, Turkey"},{"name":"Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan"},{"name":"Institute of Space-Sciences, Magurele-Bucharest 077125, Romania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6862-1634","authenticated-orcid":false,"given":"Jihad H.","family":"Asad","sequence":"additional","affiliation":[{"name":"Department of Physics, College of Applied Sciences, Palestine Technical University-Kadoorie, Tulkarm 303, Palestine"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,7,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1016\/S0022-247X(02)00394-3","article-title":"Fractional telegraph equation","volume":"276","author":"Cascaval","year":"2002","journal-title":"J. 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