Article

Unique Solvability and Existence of Eigenvalues for a Boundary Value Problem for a Parabolic-Hyperbolic Type Equation with a Fractional Derivative

B. I. IslomovNational University of Uzbekistan, Mathematical Faculty, 100174, Tashkent, UzbekistanI. A. AkhmadovNavoi State University, Faculty of Mathematics and Informatics, 210100, Navoi, Uzbekistan

Lobachevskii Journal of Mathematicsjournal2025en

ABI

Abstract

This paper investigates a boundary value problem with deviation from the characteristic (Problem $$M$$ ) for a parabolic–hyperbolic equation with a time-fractional derivative in the sense of Gerasimov–Caputo. To construct the solution of Problem $$M$$ , the first boundary value problem is solved in the parabolic part of the mixed domain, based on which the existence and uniqueness of the classical and strong solutions of Problem $$M$$ are proven. The existence of eigenvalues for the boundary value Problem $$M$$ is established.

Topics

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

Identifiers

DOI: 10.1134/s1995080225609646

Citations and references

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