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Finite-time stability analysis of fractional differential systems with variable coefficients.

Fengrong Zhang1, Deliang Qian2, Changpin Li3

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Chaos (Woodbury, N.Y.)
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This study investigates finite-time stability for fractional differential systems with variable coefficients. New theorems provide sufficient conditions for stability in both homogeneous and nonhomogeneous systems, including those with time delays.

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Area of Science:

  • Mathematics
  • Dynamical Systems
  • Control Theory

Background:

  • Fractional differential equations are increasingly used to model complex systems.
  • Understanding the stability of these systems, particularly in finite time, is crucial for their practical application.
  • Variable coefficients and time delays introduce significant challenges in stability analysis.

Purpose of the Study:

  • To analyze the finite-time stability of fractional differential systems with variable coefficients.
  • To extend stability analysis to include both homogeneous and nonhomogeneous cases.
  • To address the impact of time delays on system stability.

Main Methods:

  • Utilizing established theories of fractional differential equations.
  • Developing and applying novel mathematical theorems for stability analysis.
  • Investigating systems with and without time delays.

Main Results:

  • Three new theorems on finite-time stability were derived.
  • Sufficient conditions for finite-time stability were established for homogeneous systems without time delay.
  • Sufficient conditions were also determined for homogeneous systems with time delay.
  • Finite-time stability conditions were identified for nonhomogeneous systems with time delay.

Conclusions:

  • The study provides crucial theoretical advancements in the finite-time stability of fractional differential systems.
  • The findings offer practical tools for designing and analyzing complex dynamical systems with delays and variable coefficients.
  • This work contributes to the broader understanding of stability in fractional-order systems.