University of Guilan Journal of Mathematical Modeling 2345-394X 14 2 2026 05 01 The method based on quintic B-spline functions for addressing time-fractional advection-dispersion equations 533 556 9243 10.22124/jmm.2025.31501.2833 EN Mohamed Adel Department of Mathematics, Faculty of Science, Islamic University of Madinah, Medina, KSA. Somayieh Abdi-mazraeh Department of Applied Mathematics, Faculty of Mathematics, Statistics and Computer Sciences, University of Tabriz, Tabriz, Iran Golamreza Zaki Department of Applied Mathematics, Faculty of Mathematics, Statistics and Computer Sciences, University of Tabriz, Tabriz, Iran Safar Irandust-Pakchin Department of Mathematics Journal Article 2025 08 25 This paper introduces a numerical method designed to address the fractional time advection-dispersion equation. Initially, the time dimension is discretized by employing the L1 method. Subsequently, quintic B-spline functions are utilized for the discretization of the spatial dimension. This <br />approach yields a system of algebraic equations that can be efficiently solved. The proposed method is proven to be unconditionally stable. Numerical experiments provide compelling evidence of the method’s efficiency and effectiveness https://jmm.guilan.ac.ir/article_9243_9250861472f7a03bbcd991807a6d0570.pdf