Least squares and Instrumental Variable techniques for global identification of Fractional Differential Equation

2014 ◽  
Author(s):  
Abir Khadhraoui ◽  
Khaled Jelassi ◽  
Jean-Claude Trigeassou
Keyword(s):  
Differential Equation ◽  
Least Squares ◽  
Fractional Differential Equation ◽  
Instrumental Variable ◽  
Global Identification ◽  
Fractional Differential

scholarly journals What is the best fractional derivative to fit data?

2017 ◽  
Vol 11 (2) ◽  
pp. 358-368 ◽  
Author(s):  
Ricardo Almeida
Keyword(s):  
Differential Equation ◽  
Experimental Data ◽  
Fractional Derivative ◽  
Least Squares ◽  
Fractional Differential Equation ◽  
Fractional Derivatives ◽  
Least Squares Fitting ◽  
Different Types ◽  
Fractional Differential

The aim of this work is to show, based on concrete data observation, that the choice of the fractional derivative when modelling a problem is relevant for the accuracy of a method. Using the least squares fitting technique, we determine the order of the fractional differential equation that better describes the experimental data, for different types of fractional derivatives.

scholarly journals Convergence Analysis from the Solution of Riccati’s Fractional Differential Equation by Using Polynomial Least Squares Method

2020 ◽  
Vol 21 (1) ◽  
pp. 7-14
Author(s):  
Dian Nuryani ◽  
Endang Rusyaman ◽  
Betty Subartini
Keyword(s):  
Differential Equation ◽  
Exact Solution ◽  
Least Squares ◽  
Fractional Differential Equation ◽  
Least Squares Method ◽  
Approximate Solutions ◽  
Numerical Approach ◽  
Percentage Error ◽  
Mathematical Form ◽  
Fractional Differential

Riccati's Fractional Differential Equation (RFDE) has become a topic of study for researchers because RFDE can model variety of phenomenon in science such as random processes, optimal control and diffusion problems. Phenomena that can be modeled in a mathematical form can make it easier for humans to analyze several things from that phenomenon. RFDE generally does not have an exact solution, therefore a numerical approach solution is needed, one of the methods that gives good accuracy to the actual or exact solution is Polynomial Least Squares, where the errors calculated based on mean absolute percentage error (MAPE) produce a percentage below 1%. In addition, the convergence of a sequence from approximate solutions indicates that the sequence will converge to a solution.

scholarly journals Least Squares Differential Quadrature Method for the Generalized Bagley–Torvik Fractional Differential Equation

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Constantin Bota ◽  
Bogdan Căruntu ◽  
Mădălina Sofia Paşca ◽  
Dumitru Ţucu ◽  
Marioara Lăpădat
Keyword(s):  
Differential Equation ◽  
Least Squares ◽  
Fractional Differential Equation ◽  
Analytical Solutions ◽  
Differential Quadrature Method ◽  
Accurate Method ◽  
Differential Quadrature ◽  
Quadrature Method ◽  
Approximate Analytical Solutions ◽  
Fractional Differential

In this paper, the least squares differential quadrature method for computing approximate analytical solutions for the generalized Bagley–Torvik fractional differential equation is presented. This new method is introduced as a straightforward and accurate method, fact proved by the examples included, containing a comparison with previous results obtained by using other methods.

scholarly journals Fractional Differential Equation-Based Instantaneous Frequency Estimation for Signal Reconstruction

2021 ◽  
Vol 5 (3) ◽  
pp. 83
Author(s):  
Bilgi Görkem Yazgaç ◽  
Mürvet Kırcı
Keyword(s):  
Differential Equation ◽  
Fractional Differential Equation ◽  
Frequency Estimation ◽  
Signal Reconstruction ◽  
Reconstruction Method ◽  
Reconstruction Algorithms ◽  
Instantaneous Frequency Estimation ◽  
Proposed Model ◽  
Fractional Differential ◽  
Instantaneous Frequencies

In this paper, we propose a fractional differential equation (FDE)-based approach for the estimation of instantaneous frequencies for windowed signals as a part of signal reconstruction. This approach is based on modeling bandpass filter results around the peaks of a windowed signal as fractional differential equations and linking differ-integrator parameters, thereby determining the long-range dependence on estimated instantaneous frequencies. We investigated the performance of the proposed approach with two evaluation measures and compared it to a benchmark noniterative signal reconstruction method (SPSI). The comparison was provided with different overlap parameters to investigate the performance of the proposed model concerning resolution. An additional comparison was provided by applying the proposed method and benchmark method outputs to iterative signal reconstruction algorithms. The proposed FDE method received better evaluation results in high resolution for the noniterative case and comparable results with SPSI with an increasing iteration number of iterative methods, regardless of the overlap parameter.

scholarly journals Solutions for impulsive fractional pantograph differential equation via generalized anti-periodic boundary condition

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Idris Ahmed ◽  
Poom Kumam ◽  
Jamilu Abubakar ◽  
Piyachat Borisut ◽  
Kanokwan Sitthithakerngkiet
Keyword(s):  
Differential Equation ◽  
Boundary Condition ◽  
Fixed Point ◽  
Fractional Differential Equation ◽  
Existence And Uniqueness ◽  
Periodic Boundary Condition ◽  
Periodic Boundary ◽  
Fixed Point Theorems ◽  
Uniqueness Of The Solution ◽  
Fractional Differential

Abstract This study investigates the solutions of an impulsive fractional differential equation incorporated with a pantograph. This work extends and improves some results of the impulsive fractional differential equation. A differential equation of an impulsive fractional pantograph with a more general anti-periodic boundary condition is proposed. By employing the well-known fixed point theorems of Banach and Krasnoselskii, the existence and uniqueness of the solution of the proposed problem are established. Furthermore, two examples are presented to support our theoretical analysis.

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