Numerical Solutions of Stochastic Differential Equation Using Modified Three-Point Fractional Formula

Iqbal M. Batiha; Shaher Momani; Shameseddin Alshorm; Adel Ouannas

doi:10.1109/ICFDA58234.2023.10153192

Numerical Solutions of Stochastic Differential Equation Using Modified Three-Point Fractional Formula

Iqbal M. Batiha
, Shaher Momani
, Shameseddin Alshorm
, Adel Ouannas

Nonlinear Dynamic Research Centre (NDRC)

Al-Zaytoonah University of Jordan
University of Jordan
University of Oum El Bouaghi

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

10 Scopus citations

Abstract

This paper aims to present a numerical solution to the fractional stochastic differential equation by using modified three-point fractional formula. Such a formula, which can be derived from the generalized Taylor theorem, is used to approximate Riemann-Liouville fractional integral operator. To show the effectiveness of the numerical method, the approximate solution is compared with the exact solution coupled with the approximate solution generated from the Euler-Maruyama method. Finally, the results of numerical experiments are supported with graphs for completeness.

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/ICFDA58234.2023.10153192
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

Keywords

EulerMaruyama method
Stochastic differential equations
fractional calculus

Access to Document

10.1109/ICFDA58234.2023.10153192

Cite this

Batiha, I. M., Momani, S., Alshorm, S., & Ouannas, A. (2023). Numerical Solutions of Stochastic Differential Equation Using Modified Three-Point Fractional Formula. 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/ICFDA58234.2023.10153192

Batiha, Iqbal M. ; Momani, Shaher ; Alshorm, Shameseddin et al. / Numerical Solutions of Stochastic Differential Equation Using Modified Three-Point Fractional Formula. 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).

@inproceedings{aed36d2366b44c67adf8f302d2be7a29,

title = "Numerical Solutions of Stochastic Differential Equation Using Modified Three-Point Fractional Formula",

abstract = "This paper aims to present a numerical solution to the fractional stochastic differential equation by using modified three-point fractional formula. Such a formula, which can be derived from the generalized Taylor theorem, is used to approximate Riemann-Liouville fractional integral operator. To show the effectiveness of the numerical method, the approximate solution is compared with the exact solution coupled with the approximate solution generated from the Euler-Maruyama method. Finally, the results of numerical experiments are supported with graphs for completeness.",

keywords = "EulerMaruyama method, Stochastic differential equations, fractional calculus",

author = "Batiha, \{Iqbal M.\} and Shaher Momani and Shameseddin Alshorm and Adel Ouannas",

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/ICFDA58234.2023.10153192",

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",

}

Batiha, IM , Momani, S, Alshorm, S & Ouannas, A 2023, Numerical Solutions of Stochastic Differential Equation Using Modified Three-Point Fractional Formula. 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/ICFDA58234.2023.10153192

Numerical Solutions of Stochastic Differential Equation Using Modified Three-Point Fractional Formula. / Batiha, Iqbal M.; Momani, Shaher; Alshorm, Shameseddin et al.
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 - Numerical Solutions of Stochastic Differential Equation Using Modified Three-Point Fractional Formula

AU - Batiha, Iqbal M.

AU - Momani, Shaher

AU - Alshorm, Shameseddin

AU - Ouannas, Adel

PY - 2023

Y1 - 2023

N2 - This paper aims to present a numerical solution to the fractional stochastic differential equation by using modified three-point fractional formula. Such a formula, which can be derived from the generalized Taylor theorem, is used to approximate Riemann-Liouville fractional integral operator. To show the effectiveness of the numerical method, the approximate solution is compared with the exact solution coupled with the approximate solution generated from the Euler-Maruyama method. Finally, the results of numerical experiments are supported with graphs for completeness.

AB - This paper aims to present a numerical solution to the fractional stochastic differential equation by using modified three-point fractional formula. Such a formula, which can be derived from the generalized Taylor theorem, is used to approximate Riemann-Liouville fractional integral operator. To show the effectiveness of the numerical method, the approximate solution is compared with the exact solution coupled with the approximate solution generated from the Euler-Maruyama method. Finally, the results of numerical experiments are supported with graphs for completeness.

KW - EulerMaruyama method

KW - Stochastic differential equations

KW - fractional calculus

UR - https://www.scopus.com/pages/publications/85164540013

U2 - 10.1109/ICFDA58234.2023.10153192

DO - 10.1109/ICFDA58234.2023.10153192

M3 - Conference contribution

AN - SCOPUS:85164540013

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 -

Batiha IM , Momani S, Alshorm S, Ouannas A. Numerical Solutions of Stochastic Differential Equation Using Modified Three-Point Fractional Formula. 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/ICFDA58234.2023.10153192

Numerical Solutions of Stochastic Differential Equation Using Modified Three-Point Fractional Formula

Abstract

Publication series

Conference

Keywords

Access to Document

Other files and links

Fingerprint

Cite this