A study on variable-order delay fractional differential equations: existence, uniqueness, and numerical simulation via a predictor corrector algorithm

Abstract

In this study, we adapted a predictor-corrector technique to simulate delay differential equations incorporating variable-order Caputo-type fractional derivatives. We addressed the existence and uniqueness of solutions for the studied models. Then, we presented numerical simulation of some delay differential equations with variable-order fractional derivatives to demonstrate the efficiency of the used technique. Various periodic and chaotic characteristics of the studied models are observed for some variable-orders from the performed graphical simulations. The used technique can be modified and extended to handle different classes of initial value problems which involve variable-order fractional derivatives.