New fractional differential inequalities with their implications to the stability analysis of fractional order systems

Bichitra Kumar Lenka

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arXiv · 1903.02402

New fractional differential inequalities with their implications to the stability analysis of fractional order systems

Bichitra Kumar Lenka

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Abstract

It is well known that the Leibniz rule for the integer derivative of order one does not hold for the fractional derivative case when the fractional order lies between 0 and 1. Thus it poses a great difficulty in the calculation of fractional derivative of given functions as well as in the analysis of fractional order systems. In this work, we develop a few fractional differential inequalities which involve the Caputo fractional derivative of the product of continuously differentiable functions. We establish some of their properties and propose a few propositions. We show that these inequalities play a very essential role in the Lyapunov stability analysis of nonautonomous fractional order systems.

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Bichitra Kumar Lenka. 2019-03-05. New fractional differential inequalities with their implications to the stability analysis of fractional order systems. https://arxiv.org/abs/1903.02402

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