Generalized fractional Dirac type operators

Joel E. Restrepo; Michael Ruzhansky; Durvudkhan Suragan

doi:10.1007/s13540-023-00209-5

Generalized fractional Dirac type operators

Joel E. Restrepo
, Michael Ruzhansky
, Durvudkhan Suragan

Department of Mathematics

Ghent University
Queen Mary University of London
Nazarbayev University

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

2 Citations (Scopus)

Abstract

We introduce a class of fractional Dirac type operators with time variable coefficients by means of a Witt basis, the Djrbashian–Caputo fractional derivative and the fractional Laplacian, both operators defined with respect to some given functions. Direct and inverse fractional Cauchy type problems are studied for the introduced operators. We give explicit solutions of the considered fractional Cauchy type problems. We also use a recent method to recover a variable coefficient solution of some inverse fractional wave and heat type equations. Illustrative examples are provided.

Original language	English
Pages (from-to)	2720-2756
Number of pages	37
Journal	Fractional Calculus and Applied Analysis
Volume	26
Issue number	6
DOIs	https://doi.org/10.1007/s13540-023-00209-5
Publication status	Published - Dec 2023

Funding

First and third authors were supported by the Nazarbayev University Program 20122022CRP1601. The first and second authors were supported by the FWO Odysseus 1 grant G.0H94.18N: Analysis and Partial Differential Equations and by the Methusalem programme of the Ghent University Special Research Fund (BOF) (Grant number 01M01021). MR is also supported by EPSRC grant EP/R003025/2 and FWO Senior Research Grant G011522N. This research is funded by the Committee of Science of the Ministry of Science and Higher Education of the Republic of Kazakhstan (Grant number BR21882172).

Funders	Funder number
Ghent University Special Research Fund
Nazarbayev University	20122022CRP1601
Engineering and Physical Sciences Research Council	G011522N, EP/R003025/2
Fonds Wetenschappelijk Onderzoek (FWO)
Ministry of Education and Science of the Republic of Kazakhstan	BR21882172
Bijzonder Onderzoeksfonds UGent	01M01021

Keywords

Cauchy problem
Dirac type operators
Fractional integro-differential operator (primary)
Inverse problem

ASJC Scopus subject areas

Analysis
Applied Mathematics

Access to Document

10.1007/s13540-023-00209-5

Cite this

@article{bbbac120d42140a2b18b7e98813c0f7e,

title = "Generalized fractional Dirac type operators",

abstract = "We introduce a class of fractional Dirac type operators with time variable coefficients by means of a Witt basis, the Djrbashian{\textendash}Caputo fractional derivative and the fractional Laplacian, both operators defined with respect to some given functions. Direct and inverse fractional Cauchy type problems are studied for the introduced operators. We give explicit solutions of the considered fractional Cauchy type problems. We also use a recent method to recover a variable coefficient solution of some inverse fractional wave and heat type equations. Illustrative examples are provided.",

keywords = "Cauchy problem, Dirac type operators, Fractional integro-differential operator (primary), Inverse problem",

author = "Restrepo, \{Joel E.\} and Michael Ruzhansky and Durvudkhan Suragan",

note = "Publisher Copyright: {\textcopyright} 2023, Diogenes Co.Ltd.",

year = "2023",

month = dec,

doi = "10.1007/s13540-023-00209-5",

language = "English",

volume = "26",

pages = "2720--2756",

journal = "Fractional Calculus and Applied Analysis",

issn = "1311-0454",

publisher = "Springer International Publishing AG",

number = "6",

}

TY - JOUR

T1 - Generalized fractional Dirac type operators

AU - Restrepo, Joel E.

AU - Ruzhansky, Michael

AU - Suragan, Durvudkhan

PY - 2023/12

Y1 - 2023/12

N2 - We introduce a class of fractional Dirac type operators with time variable coefficients by means of a Witt basis, the Djrbashian–Caputo fractional derivative and the fractional Laplacian, both operators defined with respect to some given functions. Direct and inverse fractional Cauchy type problems are studied for the introduced operators. We give explicit solutions of the considered fractional Cauchy type problems. We also use a recent method to recover a variable coefficient solution of some inverse fractional wave and heat type equations. Illustrative examples are provided.

AB - We introduce a class of fractional Dirac type operators with time variable coefficients by means of a Witt basis, the Djrbashian–Caputo fractional derivative and the fractional Laplacian, both operators defined with respect to some given functions. Direct and inverse fractional Cauchy type problems are studied for the introduced operators. We give explicit solutions of the considered fractional Cauchy type problems. We also use a recent method to recover a variable coefficient solution of some inverse fractional wave and heat type equations. Illustrative examples are provided.

KW - Cauchy problem

KW - Dirac type operators

KW - Fractional integro-differential operator (primary)

KW - Inverse problem

UR - https://www.scopus.com/pages/publications/85174909602

UR - https://www.scopus.com/pages/publications/85174909602#tab=citedBy

U2 - 10.1007/s13540-023-00209-5

DO - 10.1007/s13540-023-00209-5

M3 - Article

AN - SCOPUS:85174909602

SN - 1311-0454

VL - 26

SP - 2720

EP - 2756

JO - Fractional Calculus and Applied Analysis

JF - Fractional Calculus and Applied Analysis

IS - 6

ER -

Generalized fractional Dirac type operators

Abstract

Funding

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this