Title : ( A generalized Legendre–Gauss collocation method for solving nonlinear fractional differential equations with time varying delays )
Authors: Seyed Ali Rakhshan , Sohrab Effati ,
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Abstract
We introduce a new numerical plan for nonlinear autonomous fractional differential equations with time varying delay. Generalized Legendre polynomials and their properties are developed for deriving a general procedure for solving a class of fractional differential equations. The application of the Laplace transform and generalized Legendre polynomials for solving the fractional differential equations with time varying delays is explained. Also, the properties and convergence of the proposed method are surveyed by some theorems. Finally, some numerical examples are implemented to show the efficiency and accuracy of the proposed method. The numerical result shows that the suggested method has high accuracy compared with the existing methods.
Keywords
Fractional calculus Caputo fractional derivatives Laplace transform Generalized Legendre–Gauss collocation method Fractional differential equation with delay
@article{paperid:1075481,
author = {Rakhshan, Seyed Ali and Effati, Sohrab},
title = {A generalized Legendre–Gauss collocation method for solving nonlinear fractional differential equations with time varying delays},
journal = {Applied Numerical Mathematics},
year = {2019},
volume = {146},
month = {July},
issn = {0168-9274},
pages = {342--360},
numpages = {18},
keywords = {Fractional calculus
Caputo fractional derivatives
Laplace transform
Generalized Legendre–Gauss collocation method
Fractional differential equation with delay},
}
%0 Journal Article
%T A generalized Legendre–Gauss collocation method for solving nonlinear fractional differential equations with time varying delays
%A Rakhshan, Seyed Ali
%A Effati, Sohrab
%J Applied Numerical Mathematics
%@ 0168-9274
%D 2019
