On a numerical solution for fractional differential equation within B-spline operational matrix

2014 ◽  
Author(s):  
Hossein Jafari ◽  
Haleh Tajadodi ◽  
Dumitru Baleanu
Keyword(s):  
Differential Equation ◽  
Numerical Solution ◽  
Fractional Differential Equation ◽  
Operational Matrix ◽  
B Spline ◽  
Fractional Differential

scholarly journals Numerical solution of fractional differential equation by wavelets and hybrid functions

2018 ◽  
Vol 36 (2) ◽  
pp. 231 ◽  
Author(s):  
Amir Hosein Refahi Sheikhani ◽  
Mahamad Mashoof
Keyword(s):  
Differential Equation ◽  
Fractional Differential Equation ◽  
Fractional Order ◽  
Legendre Polynomials ◽  
Linear Equations ◽  
Operational Matrix ◽  
Numerical Examples ◽  
Hybrid Functions ◽  
Block Pulse Functions ◽  
Fractional Differential

In this paper, we introduce methods based on operational matrix of fractional order integration for solving a typical n-term non-homogeneous fractional differential equation (FDE). We use Block pulse wavelets matrix of fractional order integration where a fractional derivative is defined in the Caputo sense. Also we consider Hybrid of Block-pulse functions and shifted Legendre polynomials to approximate functions. By uses these methods we translate an FDE to an algebraic linear equations which can be solve. Methods has been tested by some numerical examples.

scholarly journals An Operational Matrix of Fractional Differentiation of the Second Kind of Chebyshev Polynomial for Solving Multiterm Variable Order Fractional Differential Equation

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Jianping Liu ◽  
Xia Li ◽  
Limeng Wu
Keyword(s):  
Differential Equation ◽  
Fractional Differential Equation ◽  
Chebyshev Polynomial ◽  
Algebraic System ◽  
Operational Matrix ◽  
Main Idea ◽  
Operational Matrices ◽  
Variable Order ◽  
Fractional Differential ◽  
Variable Order Fractional Derivative

The multiterm fractional differential equation has a wide application in engineering problems. Therefore, we propose a method to solve multiterm variable order fractional differential equation based on the second kind of Chebyshev Polynomial. The main idea of this method is that we derive a kind of operational matrix of variable order fractional derivative for the second kind of Chebyshev Polynomial. With the operational matrices, the equation is transformed into the products of several dependent matrices, which can also be viewed as an algebraic system by making use of the collocation points. By solving the algebraic system, the numerical solution of original equation is acquired. Numerical examples show that only a small number of the second kinds of Chebyshev Polynomials are needed to obtain a satisfactory result, which demonstrates the validity of this method.

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