A Numerical Scheme for Solving Time-Fractional Bessel Differential Equations

Abstract

The object of this paper devotes on offering an indirect schemebased on time-fractional Bernoulli functions in the sense ofRieman-Liouville fractional derivative which ends up to the highcredit of the obtained approximate fractional Bessel solutions. Inthis paper, the operational matrices of fractional Rieman-Liouvilleintegration for Bernoulli polynomials are introduced. Utilizingthese operational matrices along with the properties of Bernoullipolynomials and the least squares method, the fractional Besseldifferential equation converts into a nonlinear system of algebraic.To solve these nonlinear algebraic equations which are a prominentproblem, there is a need to employ Newton's iterative method. Inorder to elaborate the study, the synergy of the proposed method isinvestigated and then the accuracy and the efficiency of the methodare clearly evaluated by presenting numerical results