On the Hadamard and Marchaud–Hadamard-types mixed fractional integro-differentiation

The paper is devoted to the integral representations of the Marchaud-Hadamard and Marchaud-Hadamard-type truncated mixed fractional derivatives in weighted mixed Lebesgue spaces. Inversion theorems and characterization of tne Hadamard and Hadamard-type mixed fractional integrals of functions in weighted mixed Lebesgue spaces are proven.