scholarly journals Comment on “Lie symmetries and group classification of a class of time fractional evolution systems” [J. Math. Phys. 56, 123504 (2015)]

2017 ◽  
Vol 58 (5) ◽  
pp. 054101 ◽  
Author(s):  
Komal Singla ◽  
R. K. Gupta
Keyword(s):  
Group Classification ◽  
Lie Symmetries ◽  
Fractional Evolution Systems ◽  
Evolution Systems ◽  
Math Phys

scholarly journals Lie symmetries of generalized Kawahara equations

2020 ◽  
pp. 3-10
Author(s):  
O.O. Vaneeva ◽  
◽  
A.Yu. Zhalij ◽  
Keyword(s):  
Variable Coefficients ◽  
Lie Symmetry ◽  
Group Classification ◽  
Lie Symmetries

We carry out the group classification of a normalized class of generalized Kawahara equations with variable coefficients. Admissible transformations are studied, and the partition of the class into two normalized subclasses is performed. For each of these subclasses, the respective equivalence groupoids are found. As a result, all equations from the class admitting Lie symmetry extensions are revealed.

scholarly journals On the finite approximate controllability for Hilfer fractional evolution systems with nonlocal conditions

2020 ◽  
Vol 18 (1) ◽  
pp. 529-539
Author(s):  
Xianghu Liu
Keyword(s):  
Approximate Controllability ◽  
Nonlocal Conditions ◽  
Sufficient Conditions ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Evolution System ◽  
Controlled Systems ◽  
Uniqueness Of The Solution ◽  
Fractional Evolution Systems ◽  
Evolution Systems

Abstract The aim of this study is to investigate the finite approximate controllability of certain Hilfer fractional evolution systems with nonlocal conditions. To achieve this, we first transform the mild solution of the Hilfer fractional evolution system into a fixed point problem for a condensing map. Then, by using the topological degree approach, we present sufficient conditions for the existence and uniqueness of the solution of the Hilfer fractional evolution systems. Using the variational approach, we obtain sufficient conditions for the finite approximate controllability of semilinear controlled systems. Finally, an example is provided to illustrate main results.

Lie group classification of the N-th-order nonlinear evolution equations

2011 ◽  
Vol 54 (12) ◽  
pp. 2553-2572 ◽  
Author(s):  
ShouFeng Shen ◽  
ChangZheng Qu ◽  
Qing Huang ◽  
YongYang Jin
Keyword(s):  
Lie Group ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Group Classification ◽  
Nonlinear Evolution Equations ◽  
Lie Group Classification

scholarly journals Group Classification of a General Bond-Option Pricing Equation of Mathematical Finance

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Tanki Motsepa ◽  
Chaudry Masood Khalique ◽  
Motlatsi Molati
Keyword(s):  
Option Pricing ◽  
Three Dimensional ◽  
Mathematical Finance ◽  
Group Classification ◽  
Lie Point Symmetries ◽  
Group Invariant ◽  
Black Scholes ◽  
Group Invariant Solutions ◽  
Bond Option

We carry out group classification of a general bond-option pricing equation. We show that the equation admits a three-dimensional equivalence Lie algebra. We also show that some of the values of the constants which result from group classification give us well-known models in mathematics of finance such as Black-Scholes, Vasicek, and Cox-Ingersoll-Ross. For all such values of these arbitrary constants we obtain Lie point symmetries. Symmetry reductions are then obtained and group invariant solutions are constructed for some cases.

Lie group classification of second-order ordinary difference equations

2000 ◽  
Vol 41 (1) ◽  
pp. 480-504 ◽  
Author(s):  
Vladimir Dorodnitsyn ◽  
Roman Kozlov ◽  
Pavel Winternitz
Keyword(s):  
Lie Group ◽  
Difference Equations ◽  
Group Classification ◽  
Second Order ◽  
Lie Group Classification

scholarly journals Abductive Networks For Two-Group Classification: A Comparison With Neural Networks

2011 ◽  
Vol 15 (2) ◽  
pp. 1 ◽  
Author(s):  
Anurag Agarwal
Keyword(s):  
Neural Networks ◽  
Linear Mapping ◽  
Group Classification ◽  
Type Ii ◽  
Artificial Intelligence Technique ◽  
Empirical Tests ◽  
Multivariate Discriminant ◽  
Better Than

<span>In this study, a new Artificial Intelligence technique for non-linear mapping called Abductive Networks is used for two-group classification of firms. The results are compared with Neural Networks, another AI technique, which has been shown to perform better than the traditional statistical techniques such as multivariate discriminant analysis and logit. In empirical tests, Abductive Networks perform as well or better than Neural Networks on various criteria of measurement such as Type 1 / Type II accuracy criteria and Distance Between Centroids.</span>

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