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- Title
Picard’s Iterative Method for Caputo Fractional Differential Equations with Numerical Results.
- Authors
Lyons, Rainey; Vatsala, Aghalaya S.; Chiquet, Ross A.
- 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.
- Subjects
FRACTIONAL differential equations; INITIAL value problems; ECOLOGICAL models; GAMMA functions; FRACTIONAL calculus
- Publication
Mathematics (2227-7390), 2017, Vol 5, Issue 4, p65
- ISSN
2227-7390
- Publication type
Article
- DOI
10.3390/math5040065