Solvability of the Cauchy problem for a fractionally loaded equation with variable coefficients

Shilpi Jain; Umida Baltaeva; Zebo Egamberganova; Hamrobek Hayitbayev; Praveen Agarwal; Florence Hubert; Clemente Cesarano

doi:10.1016/B978-0-44-336484-6.00019-9

Solvability of the Cauchy problem for a fractionally loaded equation with variable coefficients

Shilpi Jain
, Umida Baltaeva
, Zebo Egamberganova
, Hamrobek Hayitbayev
, Praveen Agarwal
, Florence Hubert
, Clemente Cesarano

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

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

Abstract

In this chapter, we study the well-posed problem for a heat equation with variable coefficients, including derivative and loaded terms in Holder spaces. In the problem under consideration, the loaded term is under the action of the fractional Riemann-Liouville integral operator. We will prove the unique solvability of the problem and construct a representation of the solution using the method of integral equations.

Original language	English
Title of host publication	Extended Hypergeometric Functions and Orthogonal Polynomials
Publisher	Elsevier
Pages	163-171
Number of pages	9
ISBN (Electronic)	9780443364846
ISBN (Print)	9780443364853
DOIs	https://doi.org/10.1016/B978-0-44-336484-6.00019-9
State	Published - 1 Jan 2026
Externally published	Yes

Keywords

Cauchy problem
Fractional operator
Fundamental solution
Heat equation
Loaded equation

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10.1016/B978-0-44-336484-6.00019-9

Cite this

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abstract = "In this chapter, we study the well-posed problem for a heat equation with variable coefficients, including derivative and loaded terms in Holder spaces. In the problem under consideration, the loaded term is under the action of the fractional Riemann-Liouville integral operator. We will prove the unique solvability of the problem and construct a representation of the solution using the method of integral equations.",

keywords = "Cauchy problem, Fractional operator, Fundamental solution, Heat equation, Loaded equation",

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T1 - Solvability of the Cauchy problem for a fractionally loaded equation with variable coefficients

AU - Jain, Shilpi

AU - Baltaeva, Umida

AU - Egamberganova, Zebo

AU - Hayitbayev, Hamrobek

AU - Agarwal, Praveen

AU - Hubert, Florence

AU - Cesarano, Clemente

PY - 2026/1/1

Y1 - 2026/1/1

N2 - In this chapter, we study the well-posed problem for a heat equation with variable coefficients, including derivative and loaded terms in Holder spaces. In the problem under consideration, the loaded term is under the action of the fractional Riemann-Liouville integral operator. We will prove the unique solvability of the problem and construct a representation of the solution using the method of integral equations.

AB - In this chapter, we study the well-posed problem for a heat equation with variable coefficients, including derivative and loaded terms in Holder spaces. In the problem under consideration, the loaded term is under the action of the fractional Riemann-Liouville integral operator. We will prove the unique solvability of the problem and construct a representation of the solution using the method of integral equations.

KW - Cauchy problem

KW - Fractional operator

KW - Fundamental solution

KW - Heat equation

KW - Loaded equation

UR - https://www.scopus.com/pages/publications/105032962986

U2 - 10.1016/B978-0-44-336484-6.00019-9

DO - 10.1016/B978-0-44-336484-6.00019-9

M3 - Chapter

AN - SCOPUS:105032962986

SN - 9780443364853

SP - 163

EP - 171

BT - Extended Hypergeometric Functions and Orthogonal Polynomials

PB - Elsevier

ER -

Solvability of the Cauchy problem for a fractionally loaded equation with variable coefficients

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Keywords

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