Next Article in Journal
On Edge Irregular Reflexive Labellings for the Generalized Friendship Graphs
Previous Article in Journal
Generalized Langevin Equation and the Prabhakar Derivative
Open AccessArticle

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

Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA 70504, USA
*
Authors to whom correspondence should be addressed.
Mathematics 2017, 5(4), 65; https://doi.org/10.3390/math5040065
Received: 19 October 2017 / Revised: 10 November 2017 / Accepted: 13 November 2017 / Published: 21 November 2017
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
Show Figures

Figure 1

MDPI and ACS Style

Lyons, R.; Vatsala, A.S.; Chiquet, R.A. Picard’s Iterative Method for Caputo Fractional Differential Equations with Numerical Results. Mathematics 2017, 5, 65.

Show more citation formats Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Search more from Scilit
 
Search
Back to TopTop