RETRACTED ARTICLE: Solutions of Bagley–Torvik and Painlevé equations of fractional order using iterative reproducing kernel algorithm with error estimates

This paper presents iterative reproducing kernel algorithm for obtaining the numerical solutions of Bagley–Torvik and Painlevé equations of fractional order. The representation of the exact and the numerical solutions is given in the W ^ 2 3 0 , 1 , W 2 3 0 , 1 , and W 2 1 0 , 1 inner product spaces...

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Bibliographic Details
Published in:Neural computing & applications Vol. 29; no. 5; pp. 1465 - 1479
Main Authors: Abu Arqub, Omar, Maayah, Banan
Format: Journal Article
Language:English
Published: London Springer London 01.03.2018
Springer Nature B.V
Subjects:
Artificial Intelligence
Computational Biology/Bioinformatics
Computational Science and Engineering
Computer Science
Data Mining and Knowledge Discovery
Image Processing and Computer Vision
Original Article
Probability and Statistics in Computer Science
Bagley–Torvik equation
34B15
35F10
Reproducing kernel algorithm
Fourier series expansion
Painlevé equation
47B32
Fractional-order derivative
34A08
ISSN:0941-0643, 1433-3058
Online Access:Get full text
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Summary:This paper presents iterative reproducing kernel algorithm for obtaining the numerical solutions of Bagley–Torvik and Painlevé equations of fractional order. The representation of the exact and the numerical solutions is given in the W ^ 2 3 0 , 1 , W 2 3 0 , 1 , and W 2 1 0 , 1 inner product spaces. The computation of the required grid points is relying on the R ^ t 3 s , R t 3 s , and R t 1 s reproducing kernel functions. An efficient construction is given to obtain the numerical solutions for the equations together with an existence proof of the exact solutions based upon the reproducing kernel theory. Numerical solutions of such fractional equations are acquired by interrupting the n -term of the exact solutions. In this approach, numerical examples were analyzed to illustrate the design procedure and confirm the performance of the proposed algorithm in the form of tabulate data, numerical comparisons, and graphical results. Finally, the utilized results show the significant improvement in the algorithm while saving the convergence accuracy and time.
Bibliography:ObjectType-Correction/Retraction-1
SourceType-Scholarly Journals-1
content type line 14
ISSN:0941-0643
1433-3058
DOI:10.1007/s00521-016-2484-4