Numerical simulation of nonlinear fractional delay differential equations with Mittag-Leffler kernels

Abstract

This study is concerned with finding numerical solutions of nonlinear delay differential equations involving extended Mittag-Leffler fractional derivatives of the Caputo-type. The main benefit of the used extension is to address the complexity resulting from the limitations of using fractional derivatives with non-singular Mittag-Leffler kernels. We discussed the existence and uniqueness of solutions for the studied delay models. Next, we modified an Adams-type method to numerically solve fractional delay differential equations combined with Mittag-Leffler kernels. A new type of solution belonging to the L1 space is presented for the studied models using the proposed scheme.