scholarly journals Inverse Source Problems for Degenerate Time-Fractional PDE

2022 ◽  
Vol 8 (1) ◽  
pp. 39-52
Keyword(s):  
Fractional Pde ◽  
Inverse Source Problems

MILD SOLUTIONS OF A FRACTIONAL PDE WITH NOISE

Authorea ◽  
2020 ◽  
Author(s):  
Noureddine Bouteraa ◽  
Mustafa Inc ◽  
Mehmet Ali Akinlar
Keyword(s):  
Mild Solutions ◽  
Fractional Pde

scholarly journals State and output feedback boundary control of time fractional PDE–fractional ODE cascades with space‐dependent diffusivity

2020 ◽  
Vol 14 (20) ◽  
pp. 3589-3600
Author(s):  
Juan Chen ◽  
Aleksei Tepljakov ◽  
Eduard Petlenkov ◽  
YangQuan Chen ◽  
Bo Zhuang
Keyword(s):  
Boundary Control ◽  
Output Feedback ◽  
Fractional Pde

scholarly journals SOLVING SYSTEMS OF FRACTIONAL PARTIAL DIFFERENTIAL EQUATIONS VIA TWO DIMENSIONAL LAPLACE TRANSFORMS

2020 ◽  
Vol 5 (12) ◽  
pp. 406-420
Author(s):  
A. Aghili ◽  
M.R. Masomi
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Laplace Transform ◽  
Laplace Transforms ◽  
Heat Equations ◽  
Two Dimensional ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
Homogeneous Systems ◽  
Fractional Pde

In this article, the authors used two dimensional Laplace transform to solve non - homogeneous sub - ballistic fractional PDE and homogeneous systems of time fractional heat equations. Constructive examples are also provided.

scholarly journals Local fractional heat and wave equations with Laguerre type derivatives

2020 ◽  
Vol 24 (4) ◽  
pp. 2575-2580 ◽  
Author(s):  
Chun-Fu Wei
Keyword(s):  
Differential Equation ◽  
Bounded Domain ◽  
Wave Equations ◽  
Separation Of Variables ◽  
Fractional Pde

In this paper, we investigate a local fractional PDE with Laguerre type derivative. The considered equation represents a general extension of the classical heat and wave equations. The method of separation of variables is used to solve the differential equation defined in a bounded domain.

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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