NUMERICAL SOLUTION OF FRACTIONAL SINGULAR PERTURBATION CAUCHY PROBLEM

In this work, we consider a singularly perturbed Cauchy problem where the small parameter $ \varepsilon $ appears in the highest-order derivative term (i.e., the fractional derivative). First, we analyze some properties of the fractional singular perturbation problem. Then, a Shishkin mesh is introduced to address it, as traditional numerical methods for singularly perturbed problems may lead to numerical instability. Finally, we present numerical results demonstrating good stability and accuracy.