[HTML][HTML] Analytical solution of fractional variable order differential equations
The aim of this paper is to introduce an approach for solving fractional variable order linear
differential equations. The approach is based on switching schemes that realize different …
differential equations. The approach is based on switching schemes that realize different …
On the recursive fractional variable-order derivative: equivalent switching strategy, duality, and analog modeling
In this paper, a switching strategy for recursive fractional variable-order derivative is
proposed. This strategy can be interpreted as an explanation of order switching mechanism …
proposed. This strategy can be interpreted as an explanation of order switching mechanism …
Triple estimation of fractional variable order, parameters, and state variables based on the unscented fractional order Kalman Filter
In this paper, a method for states, parameters, and fractional order estimation is presented.
The proposed method is an extension of the traditional dual estimation method and uses …
The proposed method is an extension of the traditional dual estimation method and uses …
An alternative recursive fractional variable-order derivative definition and its analog validation
The paper presents an alternative recursive definition of fractional variable-order derivative
(so-called ε-type) and its switching scheme. Nextly, an analog realization equivalent to this …
(so-called ε-type) and its switching scheme. Nextly, an analog realization equivalent to this …
Numerical schemes for initialized constant and variable fractional-order derivatives: matrix approach and its analog verification
This paper presents a method for including initial conditions in recursive constant and
variable fractional-order derivatives. The initial conditions are assumed to be in the form of a …
variable fractional-order derivatives. The initial conditions are assumed to be in the form of a …
[PDF][PDF] Duality of variable fractional order difference operators and its application in identification
D Sierociuk, M Twardy - Bulletin of the Polish Academy of …, 2014 - bibliotekanauki.pl
The paper presents a number of definitions of variable order difference and discusses
duality among some of them. The duality is used to improve the performance of the least …
duality among some of them. The duality is used to improve the performance of the least …
Modeling heat transfer process in grid-holes structure changed in time using fractional variable order calculus
P Sakrajda, D Sierociuk - Theory and Applications of Non-integer Order …, 2017 - Springer
The paper presents results of modelling the heat transfer process in specific grid-holes
media whose geometry is changed in time. The process will be modeled based on variable …
media whose geometry is changed in time. The process will be modeled based on variable …
Switching scheme, equivalence, and analog validation of the alternative fractional variable-order derivative definition
In this paper, an alternative definition of variable-order differ-integral is proposed, both in a
difference equation and matrix form. The derivation and explanation of the identity between …
difference equation and matrix form. The derivation and explanation of the identity between …
Analog modeling of fractional switched order derivative using different switching schemes
The paper presents comparison of two different switching schemes of variable order
derivatives. The first one is additive-switching scheme, when change of order is caused by …
derivatives. The first one is additive-switching scheme, when change of order is caused by …
On a new symmetric fractional variable order derivative
The paper presents particular definitions of symmetric fractional variable order derivatives.
The AD AD and DA DA types of the fractional variable order derivatives and their properties …
The AD AD and DA DA types of the fractional variable order derivatives and their properties …