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

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...

Full description

Bibliographic Details
Main Authors: Rainey Lyons, Aghalaya S. Vatsala, Ross A. Chiquet
Format: Article
Language:English
Published: MDPI AG 2017-11-01
Series:Mathematics
Subjects:
Online Access:https://www.mdpi.com/2227-7390/5/4/65
Description
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.
ISSN:2227-7390