On the Hadamard and Marchaud-Hadamard-Types Mixed Fractional Integro-Differentiation

Abstract

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