Geodesic
Fractional-order Bessel functions with various applications
Applications of Mathematics, Tome 64 (2019) no. 6, pp. 637-662.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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 
@article{10_21136_AM_2019_0279_18,
     author = {Dehestani, Haniye and Ordokhani, Yadollah and Razzaghi, Mohsen},
     title = {Fractional-order {Bessel} functions with various applications},
     journal = {Applications of Mathematics},
     pages = {637--662},
     publisher = {mathdoc},
     volume = {64},
     number = {6},
     year = {2019},
     doi = {10.21136/AM.2019.0279-18},
     mrnumber = {4042431},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.2019.0279-18/}
}
TY  - JOUR
AU  - Dehestani, Haniye
AU  - Ordokhani, Yadollah
AU  - Razzaghi, Mohsen
TI  - Fractional-order Bessel functions with various applications
JO  - Applications of Mathematics
PY  - 2019
SP  - 637
EP  - 662
VL  - 64
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.21136/AM.2019.0279-18/
DO  - 10.21136/AM.2019.0279-18
LA  - en
ID  - 10_21136_AM_2019_0279_18
ER  - 
%0 Journal Article
%A Dehestani, Haniye
%A Ordokhani, Yadollah
%A Razzaghi, Mohsen
%T Fractional-order Bessel functions with various applications
%J Applications of Mathematics
%D 2019
%P 637-662
%V 64
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.21136/AM.2019.0279-18/
%R 10.21136/AM.2019.0279-18
%G en
%F 10_21136_AM_2019_0279_18
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. http://geodesic.mathdoc.fr/articles/10.21136/AM.2019.0279-18/

Cité par Sources :