An operational matrix based on Chelyshkov polynomials for solving multi-order fractional differential equations

The main purpose of this work is to use the Chelyshkov-collocation spectral method for the solution of multi-order fractional differential equations under the supplementary conditions. The method is based on the approximate solution in terms of Chelyshkov polynomials with unknown coefficients. The f...

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Bibliographic Details
Published in:Neural computing & applications 2018-09, Vol.30 (5), p.1369-1376
Main Authors: Talaei, Y., Asgari, M.
Format: Article
Language:English
Subjects:
Artificial Intelligence
Computational Biology/Bioinformatics
Computational Science and Engineering
Computer Science
Data Mining and Knowledge Discovery
Differential equations
Image Processing and Computer Vision
Polynomials
Probability and Statistics in Computer Science
Review Article
Spectral methods
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Summary:The main purpose of this work is to use the Chelyshkov-collocation spectral method for the solution of multi-order fractional differential equations under the supplementary conditions. The method is based on the approximate solution in terms of Chelyshkov polynomials with unknown coefficients. The framework is using transform equations and the given conditions into the matrix equations. By merging these results, a new operational matrix of fractional-order derivatives in Caputo sense is constructed. Finally, numerical results are included to show the validity and applicability of the method and comparisons are made with existing results.
ISSN:0941-0643
1433-3058
DOI:10.1007/s00521-017-3118-1