a novel mid-point upwind scheme for fractional-order singularly perturbed convection-diffusion delay differential equation

This study presents a numerical approach for solving temporal fractionalorder singularly perturbed parabolic convection-diffusion differential equations with a delay using a uniformly convergent scheme. we use the asymptotic analysis of the problem to offer a priori bounds on the exact solution and its derivatives. to discretize the problem, we use the implicit euler technique on a uniform mesh in time and the midpoint upwind finite difference approach on a piece-wise uniform mesh in space. the proposed technique has a nearly first-order uniform convergence order in both spatial and temporal dimensions. to validate the theoretical analysis of the scheme, two numerical test situations for various values of ε are explored.