<p>An axiomatic basis of integration in spaces with non-integer dimensions was first proposed by Wilson (Phys Rev D 7(10):2911–2926, 1973). Spaces with non-integer dimensions are actively used in quantum field theory, statistical physics, and models of fractal media. The self-consistent calculus of integrals and derivatives in non-integer dimensional spaces (NIDS) are proposed in the voluminous 2025 article on the calculus in non-integer dimensional space in about 200 pages. In this short paper, the NIDS generalization of the general fractional calculus (GFC) is proposed. It can also be said that in this paper, the GFC generalization of the NIDS calculus is suggested. For this generalization, the integration and differentiation in one-dimensional space are replaced by the NIDS integration and NIDS differentiation. This leads to the fact that the convolution operation, which is used in the definition of GF operators and Sonin condition, becomes non-commutative and non-associative in the general case. This complicates proofs and definitions. Therefore, only for a narrow class of such operators obtained in this way satisfy the fundamental theorems of fractional calculus. In this paper, the GF integrals and GF derivatives are proposed for the D-dimensional space with D from (0,1]. For these operators, the NIDS generalizations of the fundamental theorems of GFC are proved. Therefore, the proposed GF operators in NIDS form a fractional calculus, which can be called the GFC in NIDS.</p>