7 citations · 17 across the 8 of their papers we have counts for
11 papers
On the Leibniz rule and Laplace transform for fractional derivatives
Yiheng Wei, Da-Yan Liu, Peter W. Tse +1
Taylor series is a useful mathematical tool when describing and constructing a function. With the series representation, some properties of fractional calculus can be revealed clea…
A Novel Approach for Parameter and Differentiation Order Estimation for a Space Fractional Advection Dispersion Equation
Abeer Aldoghaither, Taous-Meriem Laleg-Kirati, Da-Yan Liu
In this paper, we propose a new approach, based on the so-called modulating functions to estimate the average velocity, the dispersion coefficient and the differentiation order in…
Direct and Inverse Source Problem for a Space Fractional Advection Dispersion Equation
Abeer Aldoghaither, Taous-Meriem Laleg-Kirati, Da-Yan Liu
In this paper, direct and inverse problems for a space fractional advection dispersion equation on a finite domain are studied. The inverse problem consists in determining the sour…
Identification of fractional order systems using modulating functions method
Da-Yan Liu, Taous-Meriem Laleg-Kirati, Olivier Gibaru +1
The modulating functions method has been used for the identification of linear and nonlinear systems. In this paper, we generalize this method to the on-line identification of frac…
Fractional order differentiation by integration with Jacobi polynomials
Da-Yan Liu, Olivier Gibaru, Wilfrid Perruquetti +1
The differentiation by integration method with Jacobi polynomials was originally introduced by Mboup, Join and Fliess. This paper generalizes this method from the integer order to…
Mathematical properties of a semi-classical signal analysis method: noisy signal case
Da-Yan Liu, Taous-Meriem Laleg-Kirati
Recently, a new signal analysis method based on a semi-classical approach has been proposed [1]. The main idea in this method is to interpret a signal as a potential of a Schroding…
Non-asymptotic fractional order differentiators via an algebraic parametric method
Dayan Liu, Olivier Gibaru, Wilfrid Perruquetti
Recently, Mboup, Join and Fliess [27], [28] introduced non-asymptotic integer order differentiators by using an algebraic parametric estimation method [7], [8]. In this paper, in o…
Convergence Rate of the Causal Jacobi Derivative Estimator
Da-Yan Liu, Olivier Gibaru, Wilfrid Perruquetti
Numerical causal derivative estimators from noisy data are essential for real time applications especially for control applications or fluid simulation so as to address the new par…
Parameters estimation of a noisy sinusoidal signal with time-varying amplitude
Da-Yan Liu, Olivier Gibaru, Wilfrid Perruquetti
In this paper, we give estimators of the frequency, amplitude and phase of a noisy sinusoidal signal with time-varying amplitude by using the algebraic parametric techniques introd…
Error analysis of a class of derivative estimators for noisy signals
Da-Yan Liu, Olivier Gibaru, Wilfrid Perruquetti
Recent algebraic parametric estimation techniques led to point-wise derivative estimates by using only the iterated integral of a noisy observation signal. In this paper, we extend…
Differentiation by integration with Jacobi polynomials
Da-Yan Liu, Olivier Gibaru, Wilfrid Perruquetti
In this paper, the numerical differentiation by integration method based on Jacobi polynomials originally introduced by Mboup, Fliess and Join is revisited in the central case wher…