ABSTRACT
In this chapter, we investigate the variable-order fractional calculus variable-order fractional calculus and the variable-order general fractional calculus variable-order general fractional calculus involving the kernel of the special functions, such as the Mittag-Leffler function Mittag-Leffler function , weak power-law function weak power-law function , Lorenzo-Hartley function Lorenzo-Hartley function , Wiman function Wiman function , Miller-Ross function Miller-Ross function and Prabhakar function Prabhakar function . The Hilfer type fractional derivatives of variable order Hilfer type fractional derivatives of variable order , the Riesz type fractional derivatives of variable order Riesz type fractional derivatives of variable order , the Feller type fractional derivatives of variable order Feller type fractional derivatives of variable order and the Richard type fractional derivatives of variable order Richard type fractional derivatives of variable order are also considered. The general fractional derivatives and general fractional integrals of the variable order general fractional integrals of the variable order involving the special functions are also discussed. The mathematical models for the relaxation and rheological models are addressed in detail.
