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...
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| Format: | Article |
| Language: | English |
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MDPI AG
2017-11-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/5/4/65 |
| _version_ | 1818256837217091584 |
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| author | Rainey Lyons Aghalaya S. Vatsala Ross A. Chiquet |
| author_facet | Rainey Lyons Aghalaya S. Vatsala Ross A. Chiquet |
| author_sort | Rainey Lyons |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-12T17:34:06Z |
| format | Article |
| id | doaj.art-8b3cdbf8f2234e45921c470a69c5de77 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-12-12T17:34:06Z |
| publishDate | 2017-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-8b3cdbf8f2234e45921c470a69c5de772022-12-22T00:17:17ZengMDPI AGMathematics2227-73902017-11-01546510.3390/math5040065math5040065Picard’s Iterative Method for Caputo Fractional Differential Equations with Numerical ResultsRainey Lyons0Aghalaya S. Vatsala1Ross A. Chiquet2Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA 70504, USADepartment of Mathematics, University of Louisiana at Lafayette, Lafayette, LA 70504, USADepartment of Mathematics, University of Louisiana at Lafayette, Lafayette, LA 70504, USAWith 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.https://www.mdpi.com/2227-7390/5/4/65Caputo fractional derivativePicard’s IterationMittag-Leffler function |
| spellingShingle | Rainey Lyons Aghalaya S. Vatsala Ross A. Chiquet Picard’s Iterative Method for Caputo Fractional Differential Equations with Numerical Results Mathematics Caputo fractional derivative Picard’s Iteration Mittag-Leffler function |
| title | Picard’s Iterative Method for Caputo Fractional Differential Equations with Numerical Results |
| title_full | Picard’s Iterative Method for Caputo Fractional Differential Equations with Numerical Results |
| title_fullStr | Picard’s Iterative Method for Caputo Fractional Differential Equations with Numerical Results |
| title_full_unstemmed | Picard’s Iterative Method for Caputo Fractional Differential Equations with Numerical Results |
| title_short | Picard’s Iterative Method for Caputo Fractional Differential Equations with Numerical Results |
| title_sort | picard s iterative method for caputo fractional differential equations with numerical results |
| topic | Caputo fractional derivative Picard’s Iteration Mittag-Leffler function |
| url | https://www.mdpi.com/2227-7390/5/4/65 |
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