uniformly convergent numerical solution for caputo fractional order singularly perturbed delay differential equation using extended cubic b-spline collocation scheme

This article presents a parameter uniform convergence numerical scheme for solving time fractional order singularly perturbed parabolic convection-diffusion differential equations with a delay. we give a priori bounds on the exact solution and its derivatives obtained through the problem’s asymp-totic analysis. the euler’s method on a uniform mesh in the time direction and the extended cubic b-spline method with a fitted operator on a uniform mesh in the spatial direction is used to discretize the problem. the fitting factor is introduced for the term containing the singular perturbation pa-rameter, and it is obtained from the zeroth-order asymptotic expansion of the exact solution. the ordinary b-splines are extended into the extended b-splines. utilizing the optimization technique, the value of μ (free param-eter, when the free parameter μ tends to zero the extended cubic b-spline reduced to convectional cubic b-spline functions) is determined. it is also demonstrated that this method is better than some existing methods in the literature.