Khasminskii Approach for ψ-Caputo Fractional Stochastic Pantograph Problem

Manar A. Alqudah; Hamid Boulares; Bahaaeldin Abdalla; Thabet Abdeljawad

doi:10.1007/s12346-023-00951-4

Khasminskii Approach for ψ-Caputo Fractional Stochastic Pantograph Problem

Manar A. Alqudah, Hamid Boulares, Bahaaeldin Abdalla, Thabet Abdeljawad^*

^*Corresponding author for this work

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

3 Citations (Scopus)

Abstract

In this manuscript, we study an averaging principle for fractional stochastic pantograph differential equations (FSDPEs) in the ψ-sense accompanied by Brownian movement. Under certain assumptions, we are able to approximate solutions for FSPEs by solutions to averaged stochastic systems in the sense of mean square. Analysis of system solutions before and after the average allows extending the classical Khasminskii approach to random fractional differential equations in the sense of ψ-Caputo.

Original language	English
Article number	100
Journal	Qualitative Theory of Dynamical Systems
Volume	23
Issue number	3
DOIs	https://doi.org/10.1007/s12346-023-00951-4
Publication status	Published - Jul 2024
Externally published	Yes

Keywords

34K20
34K30
34K40
Khasminskii approach
Pantograph problem
The averaging principle
ψ-Caputo derivative

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10.1007/s12346-023-00951-4

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title = "Khasminskii Approach for ψ-Caputo Fractional Stochastic Pantograph Problem",

abstract = "In this manuscript, we study an averaging principle for fractional stochastic pantograph differential equations (FSDPEs) in the ψ-sense accompanied by Brownian movement. Under certain assumptions, we are able to approximate solutions for FSPEs by solutions to averaged stochastic systems in the sense of mean square. Analysis of system solutions before and after the average allows extending the classical Khasminskii approach to random fractional differential equations in the sense of ψ-Caputo.",

keywords = "34K20, 34K30, 34K40, Khasminskii approach, Pantograph problem, The averaging principle, ψ-Caputo derivative",

author = "Alqudah, {Manar A.} and Hamid Boulares and Bahaaeldin Abdalla and Thabet Abdeljawad",

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T1 - Khasminskii Approach for ψ-Caputo Fractional Stochastic Pantograph Problem

AU - Alqudah, Manar A.

AU - Boulares, Hamid

AU - Abdalla, Bahaaeldin

AU - Abdeljawad, Thabet

N1 - Publisher Copyright: © The Author(s) 2024.

PY - 2024/7

Y1 - 2024/7

N2 - In this manuscript, we study an averaging principle for fractional stochastic pantograph differential equations (FSDPEs) in the ψ-sense accompanied by Brownian movement. Under certain assumptions, we are able to approximate solutions for FSPEs by solutions to averaged stochastic systems in the sense of mean square. Analysis of system solutions before and after the average allows extending the classical Khasminskii approach to random fractional differential equations in the sense of ψ-Caputo.

AB - In this manuscript, we study an averaging principle for fractional stochastic pantograph differential equations (FSDPEs) in the ψ-sense accompanied by Brownian movement. Under certain assumptions, we are able to approximate solutions for FSPEs by solutions to averaged stochastic systems in the sense of mean square. Analysis of system solutions before and after the average allows extending the classical Khasminskii approach to random fractional differential equations in the sense of ψ-Caputo.

KW - 34K20

KW - 34K30

KW - 34K40

KW - Khasminskii approach

KW - Pantograph problem

KW - The averaging principle

KW - ψ-Caputo derivative

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DO - 10.1007/s12346-023-00951-4

M3 - Article

AN - SCOPUS:85184448806

SN - 1575-5460

VL - 23

JO - Qualitative Theory of Dynamical Systems

JF - Qualitative Theory of Dynamical Systems

IS - 3

M1 - 100

ER -

Khasminskii Approach for ψ-Caputo Fractional Stochastic Pantograph Problem

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Keywords

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