scholarly journals Generalized Bessel function of Type D

2008 ◽  
Author(s):  
Nizar Demni
Keyword(s):  
Bessel Function ◽  
Type D ◽  
Generalized Bessel Function

scholarly journals An application of the generalized Bessel function

2016 ◽  
Vol 142 (1) ◽  
pp. 75-84
Author(s):  
Hanan Darwish ◽  
Abdel Moneim Lashin ◽  
Bashar Hassan
Keyword(s):  
Bessel Function ◽  
Generalized Bessel Function

scholarly journals Unified integrals involving product of multivariable polynomials and generalized Bessel functions

2019 ◽  
Vol 38 (6) ◽  
pp. 73-83
Author(s):  
K. S. Nisar ◽  
D. L. Suthar ◽  
Sunil Dutt Purohit ◽  
Hafte Amsalu
Keyword(s):  
Bessel Function ◽  
Bessel Functions ◽  
General Character ◽  
Polynomial Functions ◽  
Finite Product ◽  
Generalized Bessel Function ◽  
Integral Formulas ◽  
Generalized Bessel Functions ◽  
Multivariable Polynomial ◽  
Integral Formulae

The aim of this paper is to evaluate two integral formulas involving a finite product of the generalized Bessel function of the first kind and multivariable polynomial functions which results are expressed in terms of the generalized Lauricella functions. The major results presented here are of general character and easily reducible to unique and well-known integral formulae.

scholarly journals Certain Fractional Integral Formulas Involving the Product of Generalized Bessel Functions

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
D. Baleanu ◽  
P. Agarwal ◽  
S. D. Purohit
Keyword(s):  
Bessel Function ◽  
Fractional Integral ◽  
Bessel Functions ◽  
Fractional Integration ◽  
Fractional Integrals ◽  
General Character ◽  
Generalized Bessel Function ◽  
Integral Formulas ◽  
Generalized Bessel Functions ◽  
Special Cases

We apply generalized operators of fractional integration involving Appell’s functionF3(·)due to Marichev-Saigo-Maeda, to the product of the generalized Bessel function of the first kind due to Baricz. The results are expressed in terms of the multivariable generalized Lauricella functions. Corresponding assertions in terms of Saigo, Erdélyi-Kober, Riemann-Liouville, and Weyl type of fractional integrals are also presented. Some interesting special cases of our two main results are presented. We also point out that the results presented here, being of general character, are easily reducible to yield many diverse new and known integral formulas involving simpler functions.

scholarly journals New numerical method based on Generalized Bessel function to solve nonlinear Abel fractional differential equation of the first kind

2019 ◽  
Vol 8 (1) ◽  
pp. 438-448 ◽  
Author(s):  
K. Parand ◽  
M. Nikarya
Keyword(s):  
Bessel Function ◽  
Krylov Subspace ◽  
Basis Functions ◽  
Subspace Method ◽  
Algebraic Equations ◽  
Krylov Method ◽  
Generalized Bessel Function ◽  
Minimum Residual ◽  
Fractional Differential ◽  
Nonlinear Algebraic System

Abstract Fractional calculus and fractional differential equations (FDE) have many applications in different branches of sciences. But, often a real nonlinear FDE has not the exact or analytical solution and must be solved numerically. Therefore, we aim to introduce a new numerical algorithm based on generalized Bessel function of the first kind (GBF), spectral methods and Newton–Krylov subspace method to solve nonlinear FDEs. In this paper, we use the GBFs as the basis functions. Then, we introduce explicit formulas to calculate Riemann–Liouville fractional integral and derivative of GBFs that are very helpful in computation and saving time. In the presented method, a nonlinear FDE will be converted to a nonlinear system of algebraic equations using collocation method based on GBF, then the solution of this nonlinear algebraic system will be achieved by using Newton-generalized minimum residual (Newton–Krylov) method. To illustrate the reliability and efficiency of the proposed method, we apply it to solve some examples of nonlinear Abel FDE.

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