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

M. U. Yakhshiboev

Samarkand Branch, Tashkent University of Information Technologies, named after Muhammad al-Khwarizmi, 47a Shohruh Mirzo St, Samarkand, 140100, Uzbekistan

Abstract: 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.

Keywords and phrases: Hadamard-type fractional integration, mixed Lebesgue spaces, dilation operator, the Hadamard and Marchaud-Hadamard-type fractional derivatives.

MSC: 26A33, 41A35, 46E30

Received: 26.02.2020
Accepted: 09.09.2023

Language: English

DOI: 10.32523/2077-9879-2023-14-4-69-91