Article

On a Boundary Value Problem for a Third-Order Equation of Parabolic-Hyperbolic Type with a Fractional Order Operator

B. J. KadirkulovDepartment of Mathematics and Information Technologies, Tashkent State University of Oriental Studies, 100060, Tashkent, UzbekistanM. A. JalilovFerghana State University, 150100, Ferghana, Uzbekistan

Lobachevskii Journal of Mathematicsjournal2023en

ABI

Abstract

In the paper, we consider a boundary value problem for a third-order mixed differential equation of parabolic-hyperbolic type with a fractional Gerasimov–Caputo operator. Under certain conditions on the data of a problem, applying the methods of the theory of integral equations and the Green function, we prove the unique solvability of the problem. The uniqueness of the solution is proved by the method of the extremum principle, and the existence of this problem is proved by reducing it to a boundary value problem for a fractional order differential equation, as well as to the Volterra integral equation of the second kind.

Topics

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

Identifiers

DOI: 10.1134/s1995080223070223

Citations and references

Cited by 1 15 references

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