The higher-ordered nonlinear damped fractional integro-differential dynamical framework: controllability analysis

Kirti Kaushik; Anoop Kumar; Aziz Khan; Thabet Abdeljawad

doi:10.1007/s12190-025-02388-1

The higher-ordered nonlinear damped fractional integro-differential dynamical framework: controllability analysis

Kirti Kaushik, Anoop Kumar^*, Aziz Khan, Thabet Abdeljawad^*

^*Corresponding author for this work

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

Abstract

The primary objective of this work is to explore the controllability results for the higher-order nonlinear integro-differential fractional dynamical system by utilizing Caputo operator. We investigate the controllability of the system by demonstrating a controllability Grammian matrix with the help of a control function. We discuss the sufficient conditions for the considered nonlinear system concerned to be controllable by employing the successive approximation technique. In addition, an example is illustrated to emphasize the applicability of the derived results.

Original language	English
Article number	115127
Journal	Journal of Applied Mathematics and Computing
DOIs	https://doi.org/10.1007/s12190-025-02388-1
Publication status	Published - 2025
Externally published	Yes

Keywords

Caputo operator
Controllability
Fractional dynamical system
Mittag-Leffler matrix function

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10.1007/s12190-025-02388-1

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title = "The higher-ordered nonlinear damped fractional integro-differential dynamical framework: controllability analysis",

abstract = "The primary objective of this work is to explore the controllability results for the higher-order nonlinear integro-differential fractional dynamical system by utilizing Caputo operator. We investigate the controllability of the system by demonstrating a controllability Grammian matrix with the help of a control function. We discuss the sufficient conditions for the considered nonlinear system concerned to be controllable by employing the successive approximation technique. In addition, an example is illustrated to emphasize the applicability of the derived results.",

keywords = "Caputo operator, Controllability, Fractional dynamical system, Mittag-Leffler matrix function",

author = "Kirti Kaushik and Anoop Kumar and Aziz Khan and Thabet Abdeljawad",

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T1 - The higher-ordered nonlinear damped fractional integro-differential dynamical framework

T2 - controllability analysis

AU - Kaushik, Kirti

AU - Kumar, Anoop

AU - Khan, Aziz

AU - Abdeljawad, Thabet

N1 - Publisher Copyright: © The Author(s) under exclusive licence to Korean Society for Informatics and Computational Applied Mathematics 2025.

PY - 2025

Y1 - 2025

N2 - The primary objective of this work is to explore the controllability results for the higher-order nonlinear integro-differential fractional dynamical system by utilizing Caputo operator. We investigate the controllability of the system by demonstrating a controllability Grammian matrix with the help of a control function. We discuss the sufficient conditions for the considered nonlinear system concerned to be controllable by employing the successive approximation technique. In addition, an example is illustrated to emphasize the applicability of the derived results.

AB - The primary objective of this work is to explore the controllability results for the higher-order nonlinear integro-differential fractional dynamical system by utilizing Caputo operator. We investigate the controllability of the system by demonstrating a controllability Grammian matrix with the help of a control function. We discuss the sufficient conditions for the considered nonlinear system concerned to be controllable by employing the successive approximation technique. In addition, an example is illustrated to emphasize the applicability of the derived results.

KW - Caputo operator

KW - Controllability

KW - Fractional dynamical system

KW - Mittag-Leffler matrix function

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DO - 10.1007/s12190-025-02388-1

M3 - Article

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SN - 1598-5865

JO - Journal of Applied Mathematics and Computing

JF - Journal of Applied Mathematics and Computing

M1 - 115127

ER -

The higher-ordered nonlinear damped fractional integro-differential dynamical framework: controllability analysis

Abstract

Keywords

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