https://doi.org/10.1140/epjp/s13360-024-04995-6
Regular Article
New method for linearization of non-autonomous nonlinear real-order systems
Department of Mathematics, Indian Institute of Technology Guwahati, 781039, Guwahati, Assam, India
a smsbklfc@gmail.com, bkl@iitg.ac.in
Received:
5
June
2023
Accepted:
11
February
2024
Published online:
13
March
2024
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 
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.
Bichitra Kumar Lenka and Swaroop Nandan Bora have contributed equally to this work.
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