Reconstructing the Unknown Source Function of a Fractional Parabolic Equation from the Final Data with the Conformable Derivative

Omid Nikan; Ho Duy Binh; Zakieh Avazzadeh; Le Dinh Long

doi:10.3390/sym14071490

Reconstructing the Unknown Source Function of a Fractional Parabolic Equation from the Final Data with the Conformable Derivative

Omid Nikan, Ho Duy Binh, Zakieh Avazzadeh, Le Dinh Long^*

^*Corresponding author for this work

Department of Applied Mathematics

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

Abstract

The paper’s main purpose is to find the unknown source function for the conformable heat equation. In the case of (Formula presented.), we give a modified Fractional Landweber solution and explore the error between the approximate solution and the desired solution under a priori and a posteriori parameter choice rules. The error between the regularized and exact solution is then calculated in (Formula presented.), with (Formula presented.) under some reasonable Cauchy data assumptions.

Original language	English
Article number	1490
Journal	Symmetry
Volume	14
Issue number	7
DOIs	https://doi.org/10.3390/sym14071490
Publication status	Published - Jul 2022

Keywords

Fourier truncation method
Sobolev embeddings
conformable derivative
inverse initial problem
inverse source problem
parabolic equations
regularization

Access to Document

10.3390/sym14071490

Cite this

@article{3946d3a739fe44ff9cc04aabadc1980e,

title = "Reconstructing the Unknown Source Function of a Fractional Parabolic Equation from the Final Data with the Conformable Derivative",

abstract = "The paper{\textquoteright}s main purpose is to find the unknown source function for the conformable heat equation. In the case of (Formula presented.), we give a modified Fractional Landweber solution and explore the error between the approximate solution and the desired solution under a priori and a posteriori parameter choice rules. The error between the regularized and exact solution is then calculated in (Formula presented.), with (Formula presented.) under some reasonable Cauchy data assumptions.",

keywords = "Fourier truncation method, Sobolev embeddings, conformable derivative, inverse initial problem, inverse source problem, parabolic equations, regularization",

author = "Omid Nikan and Binh, {Ho Duy} and Zakieh Avazzadeh and Long, {Le Dinh}",

note = "Publisher Copyright: {\textcopyright} 2022 by the authors.",

year = "2022",

month = jul,

doi = "10.3390/sym14071490",

language = "English",

volume = "14",

journal = "Symmetry",

issn = "2073-8994",

number = "7",

}

TY - JOUR

T1 - Reconstructing the Unknown Source Function of a Fractional Parabolic Equation from the Final Data with the Conformable Derivative

AU - Nikan, Omid

AU - Binh, Ho Duy

AU - Avazzadeh, Zakieh

AU - Long, Le Dinh

PY - 2022/7

Y1 - 2022/7

N2 - The paper’s main purpose is to find the unknown source function for the conformable heat equation. In the case of (Formula presented.), we give a modified Fractional Landweber solution and explore the error between the approximate solution and the desired solution under a priori and a posteriori parameter choice rules. The error between the regularized and exact solution is then calculated in (Formula presented.), with (Formula presented.) under some reasonable Cauchy data assumptions.

AB - The paper’s main purpose is to find the unknown source function for the conformable heat equation. In the case of (Formula presented.), we give a modified Fractional Landweber solution and explore the error between the approximate solution and the desired solution under a priori and a posteriori parameter choice rules. The error between the regularized and exact solution is then calculated in (Formula presented.), with (Formula presented.) under some reasonable Cauchy data assumptions.

KW - Fourier truncation method

KW - Sobolev embeddings

KW - conformable derivative

KW - inverse initial problem

KW - inverse source problem

KW - parabolic equations

KW - regularization

UR - http://www.scopus.com/inward/record.url?scp=85137343763&partnerID=8YFLogxK

U2 - 10.3390/sym14071490

DO - 10.3390/sym14071490

M3 - Article

AN - SCOPUS:85137343763

SN - 2073-8994

VL - 14

JO - Symmetry

JF - Symmetry

IS - 7

M1 - 1490

ER -

Reconstructing the Unknown Source Function of a Fractional Parabolic Equation from the Final Data with the Conformable Derivative

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this