THE CAUCHY PROBLEM FOR THE HEAT EQUATION WITH A FRACTIONAL LOAD

Praveen Agarwal; Florence Hubert; Yves Dermenjian; Umida Baltaeva; Bobur Hasanov

doi:10.3934/dcdss.2024176

THE CAUCHY PROBLEM FOR THE HEAT EQUATION WITH A FRACTIONAL LOAD

Praveen Agarwal
, Florence Hubert
, Yves Dermenjian
, Umida Baltaeva
, Bobur Hasanov

Nonlinear Dynamic Research Centre (NDRC)

International College of Engineering
International Center for Basic and Applied Sciences
I2M
Khorezm Mamun Academy
Urgench State University

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

3 Scopus citations

Abstract

In this paper, we study the solvability of a direct problem for a multidimensional fractionally loaded heat equation in Holder spaces. In the problem under consideration, the loaded term is represented in the form of a fractional Riemann-Liouville integral operator with respect to the time variable. This study aims to prove unique solvability and construct a representation of the solution to the problem by the method of the integral equation.

Original language	English
Pages (from-to)	194-205
Number of pages	12
Journal	Discrete and Continuous Dynamical Systems - Series S
Volume	22
DOIs	https://doi.org/10.3934/dcdss.2024176
State	Published - Jan 2026

Keywords

Cauchy problem
Heat equation
fractional operator
loaded equation

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10.3934/dcdss.2024176

Cite this

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abstract = "In this paper, we study the solvability of a direct problem for a multidimensional fractionally loaded heat equation in Holder spaces. In the problem under consideration, the loaded term is represented in the form of a fractional Riemann-Liouville integral operator with respect to the time variable. This study aims to prove unique solvability and construct a representation of the solution to the problem by the method of the integral equation.",

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author = "Praveen Agarwal and Florence Hubert and Yves Dermenjian and Umida Baltaeva and Bobur Hasanov",

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AU - Hasanov, Bobur

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KW - Cauchy problem

KW - Heat equation

KW - fractional operator

KW - loaded equation

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ER -

THE CAUCHY PROBLEM FOR THE HEAT EQUATION WITH A FRACTIONAL LOAD

Abstract

Keywords

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