Averaging Principle of ABC Fractional Stochastic Differential Equations with Rosenblatt Process - Controllability Analysis

M. Lavanya; B. Sundara Vadivoo; Kottakkaran Sooppy Nisar; Yousef A. Baker El-Ebiary; Ahmed M. Shehata

doi:10.18576/amis/190118

Averaging Principle of ABC Fractional Stochastic Differential Equations with Rosenblatt Process - Controllability Analysis

M. Lavanya
, B. Sundara Vadivoo
, Kottakkaran Sooppy Nisar
, Yousef A. Baker El-Ebiary
, Ahmed M. Shehata

Mathematics

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

Abstract

The controllability analysis of an averaging technique is investigated using the Rosenblatt process for the Atangana-Baleanu- Caputo fractional derivative (ABC derivative) system. The results of the distinctive averaged system can be used to find solutions to the underlying system's problems in terms of convergence in mean square and probability. Furthermore, by employing the Banach contraction principle, controllability results are proven. Also, numerical examples are given to demonstrate the theoretical findings.

Original language	English
Pages (from-to)	209-220
Number of pages	12
Journal	Applied Mathematics and Information Sciences
Volume	19
Issue number	1
DOIs	https://doi.org/10.18576/amis/190118
State	Published - 2025

Keywords

Atangana-Baleanu Caputo Fractional Derivative
Averaging Principle
Controllability
Rosenblatt Process
Stochastic Fractional Systems

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10.18576/amis/190118

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title = "Averaging Principle of ABC Fractional Stochastic Differential Equations with Rosenblatt Process - Controllability Analysis",

abstract = "The controllability analysis of an averaging technique is investigated using the Rosenblatt process for the Atangana-Baleanu- Caputo fractional derivative (ABC derivative) system. The results of the distinctive averaged system can be used to find solutions to the underlying system's problems in terms of convergence in mean square and probability. Furthermore, by employing the Banach contraction principle, controllability results are proven. Also, numerical examples are given to demonstrate the theoretical findings.",

keywords = "Atangana-Baleanu Caputo Fractional Derivative, Averaging Principle, Controllability, Rosenblatt Process, Stochastic Fractional Systems",

author = "M. Lavanya and \{Sundara Vadivoo\}, B. and Nisar, \{Kottakkaran Sooppy\} and \{Baker El-Ebiary\}, \{Yousef A.\} and Shehata, \{Ahmed M.\}",

year = "2025",

doi = "10.18576/amis/190118",

language = "English",

volume = "19",

pages = "209--220",

journal = "Applied Mathematics and Information Sciences",

issn = "1935-0090",

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TY - JOUR

T1 - Averaging Principle of ABC Fractional Stochastic Differential Equations with Rosenblatt Process - Controllability Analysis

AU - Lavanya, M.

AU - Sundara Vadivoo, B.

AU - Nisar, Kottakkaran Sooppy

AU - Baker El-Ebiary, Yousef A.

AU - Shehata, Ahmed M.

PY - 2025

Y1 - 2025

N2 - The controllability analysis of an averaging technique is investigated using the Rosenblatt process for the Atangana-Baleanu- Caputo fractional derivative (ABC derivative) system. The results of the distinctive averaged system can be used to find solutions to the underlying system's problems in terms of convergence in mean square and probability. Furthermore, by employing the Banach contraction principle, controllability results are proven. Also, numerical examples are given to demonstrate the theoretical findings.

AB - The controllability analysis of an averaging technique is investigated using the Rosenblatt process for the Atangana-Baleanu- Caputo fractional derivative (ABC derivative) system. The results of the distinctive averaged system can be used to find solutions to the underlying system's problems in terms of convergence in mean square and probability. Furthermore, by employing the Banach contraction principle, controllability results are proven. Also, numerical examples are given to demonstrate the theoretical findings.

KW - Atangana-Baleanu Caputo Fractional Derivative

KW - Averaging Principle

KW - Controllability

KW - Rosenblatt Process

KW - Stochastic Fractional Systems

UR - https://www.scopus.com/pages/publications/85211044562

U2 - 10.18576/amis/190118

DO - 10.18576/amis/190118

M3 - Article

AN - SCOPUS:85211044562

SN - 1935-0090

VL - 19

SP - 209

EP - 220

JO - Applied Mathematics and Information Sciences

JF - Applied Mathematics and Information Sciences

IS - 1

ER -

Averaging Principle of ABC Fractional Stochastic Differential Equations with Rosenblatt Process - Controllability Analysis

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Keywords

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