General Fractional Vector Calculus

A generalization of fractional vector calculus (FVC) as a self-consistent mathematical theory is proposed to take into account general form non-locality in kernels differential and integral operators. Self-consistency involves proving generalizations all fundamental theorems for generalized In the FVC from power-law nonlocality space, we use (GFC) Luchko approach, which was published 2021. This paper following: (I) Self-consistent definitions operators: regional line gradients, surface curl operators, divergence are proposed. (II) circulation, flux volume (III) The gradient, Green’s, Stokes’ Gauss’s proved simple complex regions. (Gradient, Green, Stokes, Gauss theorems) wider class domains, surfaces curves. All these three parts allow us state that calculus, (General FVC). difficulties problems defining operators discussed nonlocal case, caused by violation standard product rule (Leibniz rule), chain (rule differentiation function composition) semigroup property. General orthogonal curvilinear coordinates, includes spherical cylindrical also