Existence and Uniqueness of Solutions for Loaded Mixed-Type Equation with Fractional Integral Operators

Umida Baltaeva; Florence Hubert; Yulduz Babajanova; Hamrobek Hayitbayev; Praveen Agarwal

doi:10.5269/bspm.77675

Existence and Uniqueness of Solutions for Loaded Mixed-Type Equation with Fractional Integral Operators

Umida Baltaeva
, Florence Hubert
, Yulduz Babajanova
, Hamrobek Hayitbayev
, Praveen Agarwal

Urgench State University
I2M
Khorezm Mamun Academy
Mamun University
Ajman University

Research output: Contribution to journal › Article › peer-review

Abstract

This paper investigates a boundary value problem for a second-order integro-differential equation of mixed parabolic-hyperbolic type with variable coefficients and fractional loading. The main focus is on establishing the existence and uniqueness of a regular solution under integral gluing conditions imposed on the line of type change. The method of integral equations is employed to study the solvability of the problem. Sufficient conditions for unique solvability are formulated and proven. The results contribute to the theory of mixed-type equations with nonlocal and fractional conditions, which are relevant in various physical models involving memory and hereditary effects.

Original language	English
Journal	Boletim da Sociedade Paranaense de Matematica
Volume	43
Issue number	1
DOIs	https://doi.org/10.5269/bspm.77675
State	Published - 9 Feb 2025
Externally published	Yes

Keywords

Boundary value problems
Riemann-Liouville fractional derivatives
existence and uniqueness
integral gluing condition
integro-differential equations
loaded equations
parabolic-hyperbolic equations

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10.5269/bspm.77675

Cite this

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abstract = "This paper investigates a boundary value problem for a second-order integro-differential equation of mixed parabolic-hyperbolic type with variable coefficients and fractional loading. The main focus is on establishing the existence and uniqueness of a regular solution under integral gluing conditions imposed on the line of type change. The method of integral equations is employed to study the solvability of the problem. Sufficient conditions for unique solvability are formulated and proven. The results contribute to the theory of mixed-type equations with nonlocal and fractional conditions, which are relevant in various physical models involving memory and hereditary effects.",

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AU - Hubert, Florence

AU - Babajanova, Yulduz

AU - Hayitbayev, Hamrobek

AU - Agarwal, Praveen

N1 - Publisher Copyright: © Soc. Paran. de Mat.

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N2 - This paper investigates a boundary value problem for a second-order integro-differential equation of mixed parabolic-hyperbolic type with variable coefficients and fractional loading. The main focus is on establishing the existence and uniqueness of a regular solution under integral gluing conditions imposed on the line of type change. The method of integral equations is employed to study the solvability of the problem. Sufficient conditions for unique solvability are formulated and proven. The results contribute to the theory of mixed-type equations with nonlocal and fractional conditions, which are relevant in various physical models involving memory and hereditary effects.

AB - This paper investigates a boundary value problem for a second-order integro-differential equation of mixed parabolic-hyperbolic type with variable coefficients and fractional loading. The main focus is on establishing the existence and uniqueness of a regular solution under integral gluing conditions imposed on the line of type change. The method of integral equations is employed to study the solvability of the problem. Sufficient conditions for unique solvability are formulated and proven. The results contribute to the theory of mixed-type equations with nonlocal and fractional conditions, which are relevant in various physical models involving memory and hereditary effects.

KW - Boundary value problems

KW - Riemann-Liouville fractional derivatives

KW - existence and uniqueness

KW - integral gluing condition

KW - integro-differential equations

KW - loaded equations

KW - parabolic-hyperbolic equations

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ER -

Existence and Uniqueness of Solutions for Loaded Mixed-Type Equation with Fractional Integral Operators

Abstract

Keywords

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