Numerical Solution for Nonlinear Time-Fractional Partial Differential Equation With Variable Coefficient Using Reproducing Kernel Hibert Space Method

2020 ◽  
Author(s):  
Nourhane Attia ◽  
Djamila Seba ◽  
Abdelkader Nour
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Numerical Solution ◽  
Variable Coefficient ◽  
Reproducing Kernel ◽  
Fractional Partial Differential Equation ◽  
Partial Differential ◽  
Space Method

scholarly journals Symmetry determination and nonlinearization of a nonlinear time-fractional partial differential equation

2020 ◽  
Vol 476 (2233) ◽  
pp. 20190564
Author(s):  
Zhi-Yong Zhang
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Lie Algebra ◽  
Infinitesimal Generator ◽  
Linear Time ◽  
Lie Symmetry ◽  
Fractional Partial Differential Equation ◽  
Partial Differential ◽  
Fractional Pde ◽  
Leading Position

We first show that the infinitesimal generator of Lie symmetry of a time-fractional partial differential equation (PDE) takes a unified and simple form, and then separate the Lie symmetry condition into two distinct parts, where one is a linear time-fractional PDE and the other is an integer-order PDE that dominates the leading position, even completely determining the symmetry for a particular type of time-fractional PDE. Moreover, we show that a linear time-fractional PDE always admits an infinite-dimensional Lie algebra of an infinitesimal generator, just as the case for a linear PDE and a nonlinear time-fractional PDE admits, at most, finite-dimensional Lie algebra. Thus, there exists no invertible mapping that converts a nonlinear time-fractional PDE to a linear one. We illustrate the results by considering two examples.

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