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Picard’s Iterative Method for Caputo Fractional Differential Equations with Numerical Results

Author

Listed:
  • Rainey Lyons

    (Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA 70504, USA)

  • Aghalaya S. Vatsala

    (Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA 70504, USA)

  • Ross A. Chiquet

    (Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA 70504, USA)

Abstract

With fractional differential equations (FDEs) rising in popularity and methods for solving them still being developed, approximations to solutions of fractional initial value problems (IVPs) have great applications in related fields. This paper proves an extension of Picard’s Iterative Existence and Uniqueness Theorem to Caputo fractional ordinary differential equations, when the nonhomogeneous term satisfies the usual Lipschitz’s condition. As an application of our method, we have provided several numerical examples.

Suggested Citation

  • Rainey Lyons & Aghalaya S. Vatsala & Ross A. Chiquet, 2017. "Picard’s Iterative Method for Caputo Fractional Differential Equations with Numerical Results," Mathematics, MDPI, vol. 5(4), pages 1-9, November.
    • Handle: RePEc:gam:jmathe:v:5:y:2017:i:4:p:65-:d:119681
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    References listed on IDEAS

    as
    1. Garrappa, Roberto, 2015. "Trapezoidal methods for fractional differential equations: Theoretical and computational aspects," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 110(C), pages 96-112.
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