scholarly journals  High-Order Jacobi Collocation Method for the Single Term Nonlinear Fractional Differential Equations 

2020 ◽  
Vol 5 (2) ◽  
pp. 205-220
Author(s):  
پیام مختاری ◽  
Keyword(s):  
Differential Equations ◽  
Collocation Method ◽  
Fractional Differential Equations ◽  
High Order ◽  
Nonlinear Fractional Differential Equations ◽  
Single Term ◽  
Fractional Differential ◽  
Jacobi Collocation Method

scholarly journals A spectral collocation method for the coupled system of nonlinear fractional differential equations

2022 ◽  
Vol 7 (4) ◽  
pp. 5670-5689
Author(s):  
Xiaojun Zhou ◽  
◽  
Yue Dai
Keyword(s):  
Differential Equations ◽  
Collocation Method ◽  
Fractional Differential Equations ◽  
Coupled System ◽  
Spectral Collocation Method ◽  
Spectral Collocation ◽  
Caputo Fractional Derivatives ◽  
Nonlinear Fractional Differential Equations ◽  
Fractional Differential ◽  
The Given

<abstract><p>This paper analyzes the coupled system of nonlinear fractional differential equations involving the caputo fractional derivatives of order $ \alpha\in(1, 2) $ on the interval (0, T). Our method of analysis is based on the reduction of the given system to an equivalent system of integral equations, then the resulting equation is discretized by using a spectral method based on the Legendre polynomials. We have constructed a Legendre spectral collocation method for the coupled system of nonlinear fractional differential equations. The error bounds under the $ L^2- $ and $ L^{\infty}- $norms is also provided, then the theoretical result is validated by a number of numerical tests.</p></abstract>

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