Inverse problem for the loaded heat conductivity equation with variable coefficients

Umida Baltaeva; Praveen Agarwal; Bobur Khasanov; Hamrobek Hayitbayev; Shilpi Jain; Florence Hubert; Clemente Cesarano

doi:10.1016/B978-0-44-336484-6.00020-5

Inverse problem for the loaded heat conductivity equation with variable coefficients

Umida Baltaeva
, Praveen Agarwal
, Bobur Khasanov
, Hamrobek Hayitbayev
, Shilpi Jain
, Florence Hubert
, Clemente Cesarano

Academy of Sciences of the Republic of Uzbekistan
Urgench State University
International College of Engineering
International Center for Basic and Applied Sciences
Khorezm Mamun Academy
Mamun University
Poornima College of Engineering
I2M
International Telematic University Uninettuno

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

Abstract

This chapter investigates an inverse problem for a diffusion equation involving fractional loaded terms and variable coefficients. The problem is equivalently reformulated as a system of loaded equations. Using this transformation, we establish the unique solvability of the inverse problem, emphasizing the identification of the multidimensional kernel associated with a loaded integro-differential heat conduction operator.

Original language	English
Title of host publication	Extended Hypergeometric Functions and Orthogonal Polynomials
Publisher	Elsevier
Pages	173-188
Number of pages	16
ISBN (Electronic)	9780443364846
ISBN (Print)	9780443364853
DOIs	https://doi.org/10.1016/B978-0-44-336484-6.00020-5
State	Published - 1 Jan 2026
Externally published	Yes

Keywords

Contraction mapping principle
Heat equation
Inverse problem
Kernel
Loaded equation
Riemann-Liouville fractional integral operator

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10.1016/B978-0-44-336484-6.00020-5

Cite this

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abstract = "This chapter investigates an inverse problem for a diffusion equation involving fractional loaded terms and variable coefficients. The problem is equivalently reformulated as a system of loaded equations. Using this transformation, we establish the unique solvability of the inverse problem, emphasizing the identification of the multidimensional kernel associated with a loaded integro-differential heat conduction operator.",

keywords = "Contraction mapping principle, Heat equation, Inverse problem, Kernel, Loaded equation, Riemann-Liouville fractional integral operator",

author = "Umida Baltaeva and Praveen Agarwal and Bobur Khasanov and Hamrobek Hayitbayev and Shilpi Jain and Florence Hubert and Clemente Cesarano",

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T1 - Inverse problem for the loaded heat conductivity equation with variable coefficients

AU - Baltaeva, Umida

AU - Agarwal, Praveen

AU - Khasanov, Bobur

AU - Hayitbayev, Hamrobek

AU - Jain, Shilpi

AU - Hubert, Florence

AU - Cesarano, Clemente

PY - 2026/1/1

Y1 - 2026/1/1

N2 - This chapter investigates an inverse problem for a diffusion equation involving fractional loaded terms and variable coefficients. The problem is equivalently reformulated as a system of loaded equations. Using this transformation, we establish the unique solvability of the inverse problem, emphasizing the identification of the multidimensional kernel associated with a loaded integro-differential heat conduction operator.

AB - This chapter investigates an inverse problem for a diffusion equation involving fractional loaded terms and variable coefficients. The problem is equivalently reformulated as a system of loaded equations. Using this transformation, we establish the unique solvability of the inverse problem, emphasizing the identification of the multidimensional kernel associated with a loaded integro-differential heat conduction operator.

KW - Contraction mapping principle

KW - Heat equation

KW - Inverse problem

KW - Kernel

KW - Loaded equation

KW - Riemann-Liouville fractional integral operator

UR - https://www.scopus.com/pages/publications/105032974583

U2 - 10.1016/B978-0-44-336484-6.00020-5

DO - 10.1016/B978-0-44-336484-6.00020-5

M3 - Chapter

AN - SCOPUS:105032974583

SN - 9780443364853

SP - 173

EP - 188

BT - Extended Hypergeometric Functions and Orthogonal Polynomials

PB - Elsevier

ER -

Inverse problem for the loaded heat conductivity equation with variable coefficients

Abstract

Keywords

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