University of Guilan Journal of Mathematical Modeling 2345-394X 12 2 2024 07 01 A novel fitted numerical scheme for time-fractional singularly perturbed convection-diffusion problems with a delay in time via cubic $B$-spline approach 215 231 7441 10.22124/jmm.2023.25969.2303 EN Worku Tilahun Aniley Department of Mathematics, Jimma University, Jimma, Ethiopia Gemechis File Duressa Department of Mathematics, Jimma University, Jimma, Ethiopia Journal Article 2023 11 08 This paper presents a uniformly convergent numerical scheme for time-fractional  singularly perturbed convection-diffusion problem with delay in time. The time-fractional derivative is considered in the Caputo sense and treated using the implicit Euler method. Then, a uniformly convergent numerical scheme based on cubic $B$-spline method is developed along the spatial direction. The technique is proved rigorously for parameter-uniform convergence. By a numerical experimentation, it is also validated that the computational result agrees with the theoretical expectation and it is also more accurate than some existing numerical methods. https://jmm.guilan.ac.ir/article_7441_d375ffad12a3f3dcb4f3a3174fd12b84.pdf