  For the first time, a general fractional calculus of arbitrary order was
proposed by Yuri Luchko in the works Mathematics 9(6) (2021) 594 and Symmetry
13(5) (2021) 755. In these works, the proposed approaches to formulate this
calculus are based either on the power of one Sonine kernel, or the convolution
of one Sonine kernel with the kernels of the integer-order integrals. To apply
general fractional calculus, it is useful to have a wider range of operators,
for example, by using the Laplace convolution of different types of kernels. In
this paper, an extended formulation of the general fractional calculus of
arbitrary order is proposed. Extension is achieved by using different types
(subsets) of pairs of operator kernels in definitions general fractional
integrals and derivatives. For this, the definition of the Luchko pair of
kernels is somewhat broadened, which leads to the symmetry of the definition of
the Luchko pair. The proposed set of kernel pairs are subsets of the Luchko set
of kernel pairs. The fundamental theorems for the proposed general fractional
derivatives and integrals are proved.
