{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,22]],"date-time":"2026-07-22T17:48:08Z","timestamp":1784742488918,"version":"3.55.0"},"reference-count":24,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2022,11,21]],"date-time":"2022-11-21T00:00:00Z","timestamp":1668988800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100002383","name":"King Saud University","doi-asserted-by":"publisher","award":["RSP-2021\/210"],"award-info":[{"award-number":["RSP-2021\/210"]}],"id":[{"id":"10.13039\/501100002383","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This paper is devoted to an innovative and efficient technique for solving space\u2013time fractional differential equations (STFPDEs). To this end, we apply the Tau method such that the bases used are interpolating scaling functions (ISFs). The operational metrics for the derivative operator and fractional integration operator are used to introduce the operational matrix for the Caputo fractional derivative. Due to some characteristics of ISFs, such as interpolation, computation costs can be significantly reduced. We investigate the convergence of the technique, and some numerical implementations show that the method is effective for solving such equations.<\/jats:p>","DOI":"10.3390\/sym14112463","type":"journal-article","created":{"date-parts":[[2022,11,21]],"date-time":"2022-11-21T03:09:30Z","timestamp":1669000170000},"page":"2463","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Interpolating Scaling Functions Tau Method for Solving Space\u2013Time Fractional Partial Differential Equations"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9394-7305","authenticated-orcid":false,"given":"Haifa","family":"Bin Jebreen","sequence":"first","affiliation":[{"name":"Department of mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7504-0424","authenticated-orcid":false,"given":"Carlo","family":"Cattani","sequence":"additional","affiliation":[{"name":"Engineering School (DEIM), University of Tuscia, Largo dell\u2019Universit a, 01100 Viterbo, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,11,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Asadzadeh, M., and Saray, B.N. (2022). On a multiwavelet spectral element method for integral equation of a generalized Cauchy problem. BIT Numer. Math., 1\u201334.","DOI":"10.1007\/s10543-022-00915-1"},{"key":"ref_2","unstructured":"Kilbas, A., Srivastava, H.M., and Trujillo, J.J. (2006). Theory and applications of fractional differential Equations (24). 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