scholarly journals NUMERICAL SOLUTION OF FRACTIONAL DIFFERENTIAL EQUATION SYSTEM USING THE MUNTZ-LEGENDRE POLYNOMIALS

2017 ◽  
Vol 115 (3) ◽  
Author(s):  
M. Aghashahi ◽  
M.R. Gandomani
Keyword(s):  
Differential Equation ◽  
Numerical Solution ◽  
Fractional Differential Equation ◽  
Legendre Polynomials ◽  
Equation System ◽  
Differential Equation System ◽  
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.

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