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Lyapunov Functions and Stability of Caputo Fractional Differential Equations with Delays

  • Ravi Agarwal
  • Snezhana Hristova
  • Donal O’Regan
Original Research
  • 59 Downloads

Abstract

The direct Lyapunov method is extended to nonlinear Caputo fractional differential equations with variable bounded delays. A brief overview of the literature on derivatives of Lyapunov functions is given and applications to fractional equations are discussed. Advantages and disadvantages are illustrated with examples. Sufficient conditions using three derivatives of Lyapunov functions are given and our results are compared with results in the literature. Also fractional order extensions of comparison principle are established.

Keywords

Caputo fractional differential equations Lyapunov functions Stability Fractional derivative of Lyapunov functions 

Notes

Acknowledgements

Research was partially supported by Fund MU17-FMI-007, University of Plovdiv Paisii Hilendarski.

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Copyright information

© Foundation for Scientific Research and Technological Innovation 2018

Authors and Affiliations

  • Ravi Agarwal
    • 1
    • 2
  • Snezhana Hristova
    • 3
  • Donal O’Regan
    • 4
  1. 1.Department of MathematicsTexas A&M University-KingsvilleKingsvilleUSA
  2. 2. Florida Institute of TechnologyMelbourneUSA
  3. 3.Department of Applied Mathematics and ModelingUniversity of Plovdiv Paisii HilendarskiPlovdivBulgaria
  4. 4.School of Mathematics, Statistics and Applied MathematicsNational University of IrelandGalwayIreland

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