Rational Approximation for Oscillatory Mittag-Leffler Function

Aljowhara H. Honain; Khaled M. Furati

doi:10.1109/ICFDA58234.2023.10153289

Rational Approximation for Oscillatory Mittag-Leffler Function

Aljowhara H. Honain^*
, Khaled M. Furati

^*Corresponding author for this work

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

3 Scopus citations

Abstract

Mittag-Leffler function Eα and its generalizations are indispensable in fractional calculus. When 1\<α<2, its behavior is so diverse since it could be nonmonotone with oscillatory profile and varying odd number of real roots. Due to these properties, it is a challenging task to approximate this function in this range of α. In this paper, we develop a rational approximation for Eα(-z),z\>0, that captures the oscillatory behavior and the roots over extended intervals. The approximation is based on decomposing $Eα into a combination of a two-parameter rootless Mittag-Leffler function and a polynomial. This type of approximations provides efficient implementations when numerically solving fractional oscillation equations.

Original language	English
Title of host publication	2023 International Conference on Fractional Differentiation and Its Applications, ICFDA 2023
Publisher	Institute of Electrical and Electronics Engineers Inc.
ISBN (Electronic)	9798350321685
DOIs	https://doi.org/10.1109/ICFDA58234.2023.10153289
State	Published - 2023
Event	2023 International Conference on Fractional Differentiation and Its Applications, ICFDA 2023 - Ajman, United Arab Emirates Duration: 14 Mar 2023 → 16 Mar 2023

Publication series

Name	2023 International Conference on Fractional Differentiation and Its Applications, ICFDA 2023

Conference

Conference	2023 International Conference on Fractional Differentiation and Its Applications, ICFDA 2023
Country/Territory	United Arab Emirates
City	Ajman
Period	14/03/23 → 16/03/23

Bibliographical note

Publisher Copyright:
© 2023 IEEE.

Keywords

Oscillatory Mittag-Leffler function
global Padé approximation
rational approximation
zeroes of Mittag-Leffler function

ASJC Scopus subject areas

Analysis
Applied Mathematics
Mathematical Physics
Numerical Analysis

Access to Document

10.1109/ICFDA58234.2023.10153289

Cite this

Honain, A. H., & Furati, K. M. (2023). Rational Approximation for Oscillatory Mittag-Leffler Function. In 2023 International Conference on Fractional Differentiation and Its Applications, ICFDA 2023 (2023 International Conference on Fractional Differentiation and Its Applications, ICFDA 2023). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ICFDA58234.2023.10153289

@inproceedings{fcb520f521574dd1b7b1ed5ba008d6cc,

title = "Rational Approximation for Oscillatory Mittag-Leffler Function",

abstract = "Mittag-Leffler function Eα and its generalizations are indispensable in fractional calculus. When 1\textbackslash{}<α<2, its behavior is so diverse since it could be nonmonotone with oscillatory profile and varying odd number of real roots. Due to these properties, it is a challenging task to approximate this function in this range of α. In this paper, we develop a rational approximation for Eα(-z),z\textbackslash{}>0, that captures the oscillatory behavior and the roots over extended intervals. The approximation is based on decomposing \$Eα into a combination of a two-parameter rootless Mittag-Leffler function and a polynomial. This type of approximations provides efficient implementations when numerically solving fractional oscillation equations.",

keywords = "Oscillatory Mittag-Leffler function, global Pad{\'e} approximation, rational approximation, zeroes of Mittag-Leffler function",

author = "Honain, \{Aljowhara H.\} and Furati, \{Khaled M.\}",

note = "Publisher Copyright: {\textcopyright} 2023 IEEE.; 2023 International Conference on Fractional Differentiation and Its Applications, ICFDA 2023 ; Conference date: 14-03-2023 Through 16-03-2023",

year = "2023",

doi = "10.1109/ICFDA58234.2023.10153289",

language = "English",

series = "2023 International Conference on Fractional Differentiation and Its Applications, ICFDA 2023",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

booktitle = "2023 International Conference on Fractional Differentiation and Its Applications, ICFDA 2023",

address = "United States",

}

Honain, AH & Furati, KM 2023, Rational Approximation for Oscillatory Mittag-Leffler Function. in 2023 International Conference on Fractional Differentiation and Its Applications, ICFDA 2023. 2023 International Conference on Fractional Differentiation and Its Applications, ICFDA 2023, Institute of Electrical and Electronics Engineers Inc., 2023 International Conference on Fractional Differentiation and Its Applications, ICFDA 2023, Ajman, United Arab Emirates, 14/03/23. https://doi.org/10.1109/ICFDA58234.2023.10153289

Rational Approximation for Oscillatory Mittag-Leffler Function. / Honain, Aljowhara H.; Furati, Khaled M.
2023 International Conference on Fractional Differentiation and Its Applications, ICFDA 2023. Institute of Electrical and Electronics Engineers Inc., 2023. (2023 International Conference on Fractional Differentiation and Its Applications, ICFDA 2023).

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

TY - GEN

T1 - Rational Approximation for Oscillatory Mittag-Leffler Function

AU - Honain, Aljowhara H.

AU - Furati, Khaled M.

PY - 2023

Y1 - 2023

N2 - Mittag-Leffler function Eα and its generalizations are indispensable in fractional calculus. When 1\<α<2, its behavior is so diverse since it could be nonmonotone with oscillatory profile and varying odd number of real roots. Due to these properties, it is a challenging task to approximate this function in this range of α. In this paper, we develop a rational approximation for Eα(-z),z\>0, that captures the oscillatory behavior and the roots over extended intervals. The approximation is based on decomposing $Eα into a combination of a two-parameter rootless Mittag-Leffler function and a polynomial. This type of approximations provides efficient implementations when numerically solving fractional oscillation equations.

AB - Mittag-Leffler function Eα and its generalizations are indispensable in fractional calculus. When 1\<α<2, its behavior is so diverse since it could be nonmonotone with oscillatory profile and varying odd number of real roots. Due to these properties, it is a challenging task to approximate this function in this range of α. In this paper, we develop a rational approximation for Eα(-z),z\>0, that captures the oscillatory behavior and the roots over extended intervals. The approximation is based on decomposing $Eα into a combination of a two-parameter rootless Mittag-Leffler function and a polynomial. This type of approximations provides efficient implementations when numerically solving fractional oscillation equations.

KW - Oscillatory Mittag-Leffler function

KW - global Padé approximation

KW - rational approximation

KW - zeroes of Mittag-Leffler function

UR - https://www.scopus.com/pages/publications/85164537245

U2 - 10.1109/ICFDA58234.2023.10153289

DO - 10.1109/ICFDA58234.2023.10153289

M3 - Conference contribution

AN - SCOPUS:85164537245

T3 - 2023 International Conference on Fractional Differentiation and Its Applications, ICFDA 2023

BT - 2023 International Conference on Fractional Differentiation and Its Applications, ICFDA 2023

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2023 International Conference on Fractional Differentiation and Its Applications, ICFDA 2023

Y2 - 14 March 2023 through 16 March 2023

ER -

Honain AH, Furati KM. Rational Approximation for Oscillatory Mittag-Leffler Function. In 2023 International Conference on Fractional Differentiation and Its Applications, ICFDA 2023. Institute of Electrical and Electronics Engineers Inc. 2023. (2023 International Conference on Fractional Differentiation and Its Applications, ICFDA 2023). doi: 10.1109/ICFDA58234.2023.10153289

Rational Approximation for Oscillatory Mittag-Leffler Function

Abstract

Publication series

Conference

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Fingerprint

Cite this