Parametric General Fractional Calculus: Nonlocal Operators Acting on Function with Respect to Another Function

Abstract: In this paper, we present the definitions and some properties of the general fractional integrals (GFIs) and general fractional derivatives (GFDs) of a function f(x) with respect to another function g(x). Examples of special cases of parametric GF operators are described. Some properties of the parametric GFIs and the parametric GFDs are proved. Representation of the parametric GFIs and parametric GFDs via the GF integrals on the finite interval (a,b). Fundamental theorems of parametric GFC are proved. Applied mathematical interpretations of parametric general fractional derivatives for processes with memory are given.