[HTML][HTML] Analytical solution of fractional variable order differential equations

W Malesza, M Macias, D Sierociuk - Journal of Computational and Applied …, 2019 - Elsevier
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 …

On the recursive fractional variable-order derivative: equivalent switching strategy, duality, and analog modeling

D Sierociuk, W Malesza, M Macias - Circuits, Systems, and Signal …, 2015 - Springer
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 …

Triple estimation of fractional variable order, parameters, and state variables based on the unscented fractional order Kalman Filter

D Sierociuk, M Macias - Sensors, 2021 - mdpi.com
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 …

An alternative recursive fractional variable-order derivative definition and its analog validation

M Macias, D Sierociuk - ICFDA'14 International Conference on …, 2014 - ieeexplore.ieee.org
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 …

Numerical schemes for initialized constant and variable fractional-order derivatives: matrix approach and its analog verification

D Sierociuk, W Malesza… - Journal of Vibration and …, 2016 - journals.sagepub.com
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 …

[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 …

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 …

Switching scheme, equivalence, and analog validation of the alternative fractional variable-order derivative definition

D Sierociuk, W Malesza… - 52nd IEEE conference on …, 2013 - ieeexplore.ieee.org
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 …

Analog modeling of fractional switched order derivative using different switching schemes

D Sierociuk, M Macias… - IEEE Journal on Emerging …, 2013 - ieeexplore.ieee.org
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 …

On a new symmetric fractional variable order derivative

D Sierociuk, W Malesza, M Macias - … of Non-Integer Order Systems: 7th …, 2015 - Springer
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 …