A Pro Rata Definition of the Fractional-Order Derivative

Ramzi B. Albadarneh; Ahmad M. Adawi; Sa’ud Al-Sa’di; Iqbal M. Batiha; Shaher Momani

doi:10.1007/978-981-99-0447-1_6

A Pro Rata Definition of the Fractional-Order Derivative

Ramzi B. Albadarneh
, Ahmad M. Adawi
, Sa’ud Al-Sa’di
, Iqbal M. Batiha
, Shaher Momani

Nonlinear Dynamic Research Centre (NDRC)

Hashemite University
Al-Zaytoonah University of Jordan

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

8 Scopus citations

Abstract

In this paper a novel definition of the fractional-order derivative operator will be introduced. This operator will be called “pro rata” due to its ratio form as well as its geometric behavior that it is proportional to the fractional-order value. Some properties and theorems will be investigated. As an inverse of the fractional-order derivative operator, the integral of fractional order will be introduced. Some illustrative examples will be given.

Original language	English
Title of host publication	Mathematics and Computation - IACMC 2022
Editors	Dia Zeidan, Juan C. Cortés, Aliaa Burqan, Ahmad Qazza, Gharib Gharib, Jochen Merker
Publisher	Springer
Pages	65-79
Number of pages	15
ISBN (Print)	9789819904464
DOIs	https://doi.org/10.1007/978-981-99-0447-1_6
State	Published - 2023
Event	7th International Arab Conference on Mathematics and Computations, IACMC 2022 - Zarqa, Jordan Duration: 11 May 2022 → 13 May 2022

Publication series

Name	Springer Proceedings in Mathematics and Statistics
Volume	418
ISSN (Print)	2194-1009
ISSN (Electronic)	2194-1017

Conference

Conference	7th International Arab Conference on Mathematics and Computations, IACMC 2022
Country/Territory	Jordan
City	Zarqa
Period	11/05/22 → 13/05/22

Keywords

Fractional derivative
Fractional integral

Access to Document

10.1007/978-981-99-0447-1_6

Cite this

Albadarneh, R. B., Adawi, A. M., Al-Sa’di, S., Batiha, I. M., & Momani, S. (2023). A Pro Rata Definition of the Fractional-Order Derivative. In D. Zeidan, J. C. Cortés, A. Burqan, A. Qazza, G. Gharib, & J. Merker (Eds.), Mathematics and Computation - IACMC 2022 (pp. 65-79). (Springer Proceedings in Mathematics and Statistics; Vol. 418). Springer. https://doi.org/10.1007/978-981-99-0447-1_6

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abstract = "In this paper a novel definition of the fractional-order derivative operator will be introduced. This operator will be called “pro rata” due to its ratio form as well as its geometric behavior that it is proportional to the fractional-order value. Some properties and theorems will be investigated. As an inverse of the fractional-order derivative operator, the integral of fractional order will be introduced. Some illustrative examples will be given.",

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Albadarneh, RB, Adawi, AM, Al-Sa’di, S, Batiha, IM & Momani, S 2023, A Pro Rata Definition of the Fractional-Order Derivative. in D Zeidan, JC Cortés, A Burqan, A Qazza, G Gharib & J Merker (eds), Mathematics and Computation - IACMC 2022. Springer Proceedings in Mathematics and Statistics, vol. 418, Springer, pp. 65-79, 7th International Arab Conference on Mathematics and Computations, IACMC 2022, Zarqa, Jordan, 11/05/22. https://doi.org/10.1007/978-981-99-0447-1_6

A Pro Rata Definition of the Fractional-Order Derivative. / Albadarneh, Ramzi B.; Adawi, Ahmad M.; Al-Sa’di, Sa’ud et al.
Mathematics and Computation - IACMC 2022. ed. / Dia Zeidan; Juan C. Cortés; Aliaa Burqan; Ahmad Qazza; Gharib Gharib; Jochen Merker. Springer, 2023. p. 65-79 (Springer Proceedings in Mathematics and Statistics; Vol. 418).

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

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