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

Rainey Lyons, Aghalaya S. Vatsala and Ross A. Chiquet
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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

Mathematics, 2017, vol. 5, issue 4, 1-9

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.

Keywords: Caputo fractional derivative; Picard’s Iteration; Mittag-Leffler function (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2017
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