On an operational matrix method based on generalized Bernoulli polynomials of level m

CALCOLO ◽  
2018 ◽  
Vol 55 (3) ◽  
Author(s):  
Yamilet Quintana ◽  
William Ramírez ◽  
Alejandro Urieles
Keyword(s):  
Matrix Method ◽  
Operational Matrix ◽  
Bernoulli Polynomials ◽  
Operational Matrix Method ◽  
Generalized Bernoulli Polynomials

scholarly journals A Reliable Method for Solving Fractional Sturm–Liouville Problems

Mathematics ◽  
2018 ◽  
Vol 6 (10) ◽  
pp. 176 ◽  
Author(s):  
M. Khashshan ◽  
Muhammed Syam ◽  
Ahlam Al Mokhmari
Keyword(s):  
Matrix Method ◽  
Reliable Method ◽  
Operational Matrix ◽  
Liouville Problem ◽  
Numerical Examples ◽  
Operational Matrix Method ◽  
Sturm Liouville

In this paper, a reliable method for solving fractional Sturm–Liouville problem based on the operational matrix method is presented. Some of our numerical examples are presented.

Fractional Chebyshev Finite Difference Method for Solving the Fractional-Order Delay BVPs

2015 ◽  
Vol 12 (06) ◽  
pp. 1550033 ◽  
Author(s):  
M. M. Khader
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Fractional Order ◽  
Difference Method ◽  
Matrix Method ◽  
Fractional Derivatives ◽  
Numerical Technique ◽  
Operational Matrix ◽  
Operational Matrix Method ◽  
Chebyshev Finite Difference Method

In this paper, we implement an efficient numerical technique which we call fractional Chebyshev finite difference method (FChFDM). The fractional derivatives are presented in terms of Caputo sense. The algorithm is based on a combination of the useful properties of Chebyshev polynomials approximation and finite difference method. The proposed technique is based on using matrix operator expressions which applies to the differential terms. The operational matrix method is derived in our approach in order to approximate the fractional derivatives. This operational matrix method can be regarded as a nonuniform finite difference scheme. The error bound for the fractional derivatives is introduced. We used the introduced technique to solve numerically the fractional-order delay BVPs. The application of the proposed method to introduced problem leads to algebraic systems which can be solved by an appropriate numerical method. Several numerical examples are provided to confirm the accuracy and the effectiveness of the proposed method.

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