Geodesic
Fractional-order Bessel functions with various applications
Applications of Mathematics, Tome 64 (2019) no. 6, pp. 637-662 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
DOI : 10.21136/AM.2019.0279-18
Classification : 34A08, 65L70, 65M70
Keywords: fractional-order Bessel functions; fractional operational matrix; error estimation 
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     title = {Fractional-order {Bessel} functions with various applications},
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Dehestani, Haniye; Ordokhani, Yadollah; Razzaghi, Mohsen. Fractional-order Bessel functions with various applications. Applications of Mathematics, Tome 64 (2019) no. 6, pp. 637-662. doi: 10.21136/AM.2019.0279-18

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