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On one of the boundaries of the considered domain, a fractional boundary condition of the third kind was adopted. In the case of the direct problem, a differential scheme was presented, and a metaheuristic optimization algorithm, namely the Group Teaching Optimization Algorithm (GTOA), was used to solve the inverse problem. The article presents numerical examples illustrating the operation of the proposed methods. In the case of inverse problem, a function occurring in the fractional boundary condition was identified. The presented approach can be an effective tool for modeling the anomalous diffusion phenomenon.<\/jats:p>","DOI":"10.3390\/e28010081","type":"journal-article","created":{"date-parts":[[2026,1,12]],"date-time":"2026-01-12T09:13:01Z","timestamp":1768209181000},"page":"81","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["An Inverse Problem for a Fractional Space\u2013Time Diffusion Equation with Fractional Boundary Condition"],"prefix":"10.3390","volume":"28","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7255-6951","authenticated-orcid":false,"given":"Rafa\u0142","family":"Brociek","sequence":"first","affiliation":[{"name":"Department of Artificial Intelligence Modelling, Faculty of Applied Mathematics, Silesian University of Technology, Kaszubska 23, 44-100 Gliwice, Poland"},{"name":"Department of Electrical, Electronics and Informatics Engineering, University of Catania, Viale Andrea Doria 6, 95125 Catania, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1667-3328","authenticated-orcid":false,"given":"Agata","family":"Wajda","sequence":"additional","affiliation":[{"name":"Institute of Energy and Fuel Processing Technology, Zamkowa 1, 41-800 Zabrze, Poland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3336-5853","authenticated-orcid":false,"given":"Christian","family":"Napoli","sequence":"additional","affiliation":[{"name":"Department of Computer, Control, and Management Engineering, Sapienza University of Rome, Via Ariosto 25, 00185 Roma, Italy"},{"name":"Department of Artificial Intelligence, Czestochowa University of Technology, Dabrowskiego 69, 42-201 Czestochowa, Poland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2555-9866","authenticated-orcid":false,"given":"Giacomo","family":"Capizzi","sequence":"additional","affiliation":[{"name":"Department of Artificial Intelligence Modelling, Faculty of Applied Mathematics, Silesian University of Technology, Kaszubska 23, 44-100 Gliwice, Poland"},{"name":"Department of Electrical, Electronics and Informatics Engineering, University of Catania, Viale Andrea Doria 6, 95125 Catania, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9265-5711","authenticated-orcid":false,"given":"Damian","family":"S\u0142ota","sequence":"additional","affiliation":[{"name":"Department of Mathematical Methods in Technology and Computer Science, Faculty of Applied Mathematics, Silesian University of Technology, Kaszubska 23, 44-100 Gliwice, Poland"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,1,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"118440","DOI":"10.1016\/j.ijheatmasstransfer.2019.118440","article-title":"Comparison of mathematical models with fractional derivative for the heat conduction inverse problem based on the measurements of temperature in porous aluminum","volume":"143","author":"Brociek","year":"2019","journal-title":"Int. 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