General Fractional Calculus with Nonsingular Kernels: New Prospective on Viscoelasticity

Abstract

In the chapter, the general fractional derivatives in the different kernel functions, such as Mittag-Lefller, Wiman and Prabhakar functions are considered to model the viscoelastic behaviors in the real materials. We investigate the basic formulas of the fractional calculus (FC) in the kernels of the power, Mittag-Lefller, Wiman and Prabhakar functions. We discuss the applications for the general fractional calculus (GFC) in viscoelasticity. As the examples, the Maxwell and Voigt models with the general fractional derivatives (GFD) are considered to represent the complexity of the real materials.