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New method for linearization of non-autonomous nonlinear real-order systems

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Abstract

The linearization approach is widely known and can be used to analyze and understand the governing flows of many real-order nonlinear systems. In this paper, we provide a new method of linearization that gives useful tools for the local and/or global asymptotic stability analysis of many such nonlinear systems defined in the sense of Caputo derivative. The new results that concern order-dependent conditions based on comparison linearization theorems with the introduction of a new \(\mathcal {L_{\infty }}\) function are proposed. The implications of the introduced theoretical approach are illustrated to a nonlinear system when initial time is negative and to a positive initial-time real-order Lorenz system.

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Acknowledgements

Bichitra Kumar Lenka acknowledges the Indian Institute of Technology Guwahati for providing essential support.

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Author notes

  1. Bichitra Kumar Lenka and Swaroop Nandan Bora have contributed equally to this work.

Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology Guwahati, Guwahati, Assam, 781039, India

    Bichitra Kumar Lenka & Swaroop Nandan Bora

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  1. Bichitra Kumar Lenka
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  2. Swaroop Nandan Bora
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The authors contributed to the study conception, design and material preparation. The authors read and approved the final manuscript.

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Correspondence to Bichitra Kumar Lenka.

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Lenka, B.K., Bora, S.N. New method for linearization of non-autonomous nonlinear real-order systems. Eur. Phys. J. Plus 139, 249 (2024). https://doi.org/10.1140/epjp/s13360-024-04995-6

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