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Mathematics 2017, 5(4), 65; https://doi.org/10.3390/math5040065

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

Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA 70504, USA
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Received: 19 October 2017 / Revised: 10 November 2017 / Accepted: 13 November 2017 / Published: 21 November 2017
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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. View Full-Text
Keywords: Caputo fractional derivative; Picard’s Iteration; Mittag-Leffler function Caputo fractional derivative; Picard’s Iteration; Mittag-Leffler function
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Lyons, R.; Vatsala, A.S.; Chiquet, R.A. Picard’s Iterative Method for Caputo Fractional Differential Equations with Numerical Results. Mathematics 2017, 5, 65.

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