University of Guilan Journal of Mathematical Modeling 2345-394X 14 1 2026 03 01 Numerical solution of the time fractional nonlinear burgers equation using the quintic B-Spline method 253 271 9140 10.22124/jmm.2025.31069.2784 EN Fahad Kamil Nashmi Department of Mathematics, College of Science, University of Basrah, Basrah, Iraq. Bushra Aziz Taha Department of Mathematics, College of Science, University of Basrah, Basrah, Iraq 0000-0002-8282-9968 Journal Article 2025 07 03 This paper introduced a novel approach for resolving fractional partial differential equations.<br />The time fractional nonlinear Burgers equation of order k was solved to illustrate the efficacy<br />of the technique, where k in (0;1]. The quintic B-spline method facilitated spatial partitioning, while the finite difference method addressed the fractional Caputo derivative, which simulates anomalous diffusion processes influenced by memory effects. The proposed methods stability is demonstrated utilizing the von Neumann technique; it has been shown to be unconditionally stable. Additionally, a convergence study is shown, demonstrating that the approach exhibits uniform convergence of (gh4 +s(Dh2)). We validated the methods correctness through numerical tests by comparing it with the exact solution and alternative numerical methods. Based on L2 and L¥ error norms, the quintic B-spline approach exhibits improved convergence rates and reduced computing costs. https://jmm.guilan.ac.ir/article_9140_6451a05084b45f9c775a3874c9a3d2b4.pdf