Picard's iterative method for Caputo fractional differential equations with numerical results
type: Item
instance of: scholarly article
title: Picard's iterative method for Caputo fractional differential equations with numerical results
author: Rainey Lyons
author: Aghalaya S. Vatsala
author: Ross A. Chiquet
published in: Mathematics
publication date: 2018-07-05T00:00:00Z
review text: Summary: 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.
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 34A08
Mathematics Subject Classification ID: 26A33
zbMATH DE Number: 6898694
zbMATH Keywords: Caputo fractional derivative
zbMATH Keywords: Picard's iteration
zbMATH Keywords: Mittag-Leffler function
describes a project that uses: ma2dfc
MaRDI profile type: Publication
full work available at URL: math5040065
OpenAlex ID: W2770825101
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DOI: 10.3390/MATH5040065
description: scientific article; zbMATH DE number 6898694