Next Article in Journal
From Fractal Behavior of Iteration Methods to an Efficient Solver for the Sign of a Matrix
Next Article in Special Issue
Fractional Stochastic Integro-Differential Equations with Nonintantaneous Impulses: Existence, Approximate Controllability and Stochastic Iterative Learning Control
Previous Article in Journal
Approximating the First Passage Time Density of Diffusion Processes with State-Dependent Jumps
Previous Article in Special Issue
Controllability of Fractional Stochastic Delay Systems Driven by the Rosenblatt Process
 
 
Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
Journals
Fractal Fract
Volume 7
Issue 1
10.3390/fractalfract7010031
fractalfract-logo
Submit to this Journal Review for this Journal Propose a Special Issue
► Article Menu

Article Menu

share Share announcement Help format_quote Cite question_answer Discuss in SciProfiles
first_page
settings
Order Article Reprints
Font Type:
Arial Georgia Verdana
Font Size:
Aa Aa Aa
Line Spacing:
Column Width:
Background:
Article

On Averaging Principle for Caputo–Hadamard Fractional Stochastic Differential Pantograph Equation

by
Mounia Mouy
1,
Hamid Boulares
2,
Saleh Alshammari
3,
Mohammad Alshammari
3,
Yamina Laskri
4 and
Wael W. Mohammed
3,5,*
1
Department of Mathematics, Faculty of Sciences, University Badji Mokhtar Annaba, P.O. Box 12, Annaba 23000, Algeria
2
Laboratory of Analysis and Control of Differential Equations “ACED”, Faculty MISM, Department of Mathematics, University of Guelma, Guelma 24000, Algeria
3
Department of Mathematics, Collage of Science, University of Ha’il, Ha’il 2440, Saudi Arabia
4
Higher School of Industrial Technologies, Annaba 23000, Algeria
5
Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
*
Author to whom correspondence should be addressed.
Fractal Fract. 2023, 7(1), 31; https://doi.org/10.3390/fractalfract7010031
Submission received: 8 December 2022 / Revised: 23 December 2022 / Accepted: 26 December 2022 / Published: 28 December 2022
(This article belongs to the Special Issue Fractional Order Systems: Deterministic and Stochastic Analysis II)
Versions Notes

Abstract

In this paper, we studied an averaging principle for Caputo–Hadamard fractional stochastic differential pantograph equation (FSDPEs) driven by Brownian motion. In light of some suggestions, the solutions to FSDPEs can be approximated by solutions to averaged stochastic systems in the sense of mean square. We expand the classical Khasminskii approach to Caputo–Hadamard fractional stochastic equations by analyzing systems solutions before and after applying averaging principle. We provided an applied example that explains the desired results to us.
Keywords: averaging principle; Caputo–Hadamard fractional derivative; pantograph equations; Khasminskii approach averaging principle; Caputo–Hadamard fractional derivative; pantograph equations; Khasminskii approach

Share and Cite

MDPI and ACS Style

Mouy, M.; Boulares, H.; Alshammari, S.; Alshammari, M.; Laskri, Y.; Mohammed, W.W. On Averaging Principle for Caputo–Hadamard Fractional Stochastic Differential Pantograph Equation. Fractal Fract. 2023, 7, 31. https://doi.org/10.3390/fractalfract7010031

AMA Style

Mouy M, Boulares H, Alshammari S, Alshammari M, Laskri Y, Mohammed WW. On Averaging Principle for Caputo–Hadamard Fractional Stochastic Differential Pantograph Equation. Fractal and Fractional. 2023; 7(1):31. https://doi.org/10.3390/fractalfract7010031

Chicago/Turabian Style

Mouy, Mounia, Hamid Boulares, Saleh Alshammari, Mohammad Alshammari, Yamina Laskri, and Wael W. Mohammed. 2023. "On Averaging Principle for Caputo–Hadamard Fractional Stochastic Differential Pantograph Equation" Fractal and Fractional 7, no. 1: 31. https://doi.org/10.3390/fractalfract7010031

APA Style

Mouy, M., Boulares, H., Alshammari, S., Alshammari, M., Laskri, Y., & Mohammed, W. W. (2023). On Averaging Principle for Caputo–Hadamard Fractional Stochastic Differential Pantograph Equation. Fractal and Fractional, 7(1), 31. https://doi.org/10.3390/fractalfract7010031

Article Metrics

Back to TopTop