Article

On a boundary value problem for a nonlocal mixed-type equation with the Hilfer operator

M. A. JalilovFergana State University, Murabbiylar str. 19, Fergana 150100, UzbekistanGavhar KayumovaFergana State University, Murabbiylar str. 19, Fergana 150100, Uzbekistan

AIP conference proceedingsjournal2021en

ABI

Abstract

In this paper, we consider a boundary value problem for a fourth-order differential equation of mixed type with involution and with Hilfer operator of fractional integro-differentiation in a rectangular domain. The mixed type differential equation under consideration is a fourth-order differential equation with respect to the second variable. Regarding the first variable, this equation is a fractional differential equation in the positive part of the segment and is a second-order differential equation in the negative part of the segment. Using the spectral method of separation of variables, the solution of the problem is constructed in the form of a Fourier series. Theorems on the existence and uniqueness of the problem are proved.

Topics

Differential Equations and Boundary Problems Differential Equations and Numerical Methods Fractional Differential Equations Solutions

Identifiers

DOI: 10.1063/5.0057197

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