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Title: Fractional-order Bessel functions with various applications (English)
Author: Dehestani, Haniye
Author: Ordokhani, Yadollah
Author: Razzaghi, Mohsen
Language: English
Journal: Applications of Mathematics
ISSN: 0862-7940 (print)
ISSN: 1572-9109 (online)
Volume: 64
Issue: 6
Year: 2019
Pages: 637-662
Summary lang: English
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Category: math
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Summary: We introduce fractional-order Bessel functions (FBFs) to obtain an approximate solution for various kinds of differential equations. Our main aim is to consider the new functions based on Bessel polynomials to the fractional calculus. To calculate derivatives and integrals, we use Caputo fractional derivatives and Riemann-Liouville fractional integral definitions. Then, operational matrices of fractional-order derivatives and integration for FBFs are derived. Also, we discuss an error estimate between the computed approximations and the exact solution and apply it in some examples. Applications are given to three model problems to demonstrate the effectiveness of the proposed method. (English)
Keyword: fractional-order Bessel functions
Keyword: fractional operational matrix
Keyword: error estimation
MSC: 34A08
MSC: 65L70
MSC: 65M70
idZBL: 07144731
idMR: MR4042431
DOI: 10.21136/AM.2019.0279-18
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Date available: 2019-12-09T11:47:32Z
Last updated: 2020-07-02
Stable URL: http://hdl.handle.net/10338.dmlcz/147926
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