5 - Variable-order general fractional derivatives with nonsingular kernels

Abstract

In this chapter, we present the variable-order fractional derivatives with nonsingular kernels, which are called the variable-order general fractional derivatives. We introduce the variable-order general fractional derivatives with Mittag-Leffler–Gauss-like, Mittag-Leffler, Wiman, Prabhakar, one-parameter Lorenzo–Hartely, and Miller–Ross nonsingular kernels. We also propose the Hilfer-type variable-order general fractional derivatives with nonsingular kernels, e.g., Mittag-Leffler, Wiman, Prabhakar, one-parameter Lorenzo–Hartely, and Miller–Ross.