a novel fitted numerical scheme for time-fractional singularly perturbed convection-diffusion problems with a delay in time via cubic b-spline approach

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.