Simple Identification of Fractional Differential Equation

2011 ◽  
Vol 180 ◽  
pp. 331-338 ◽  
Author(s):  
Wojciech Mitkowski ◽  
Anna Obrączka
Keyword(s):  
Differential Equation ◽  
Fractional Differential Equation ◽  
Numerical Experiments ◽  
Identification Problem ◽  
Marquardt Algorithm ◽  
Non Linear ◽  
Fractional Differential ◽  
Estimation Parameters

In this paper the simple identification problem for fractional differential equation of Caputo type was considered. This is the problem of estimation parameters, for which the quadratic criterion is minimized. For solving this issue, the Non Linear Programing technique, based on Marquardt algorithm, was used. At the end of article the results for numerical experiments was presented.

scholarly journals Ulam-Hyers Stability for Cauchy Fractional Differential Equation in the Unit Disk

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Rabha W. Ibrahim
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Fractional Differential Equation ◽  
Unit Disk ◽  
Fractional Differential Equations ◽  
Fractional Operators ◽  
Owa Operators ◽  
Non Linear ◽  
Fractional Differential

We prove the Ulam-Hyers stability of Cauchy fractional differential equations in the unit disk for the linear and non-linear cases. The fractional operators are taken in sense of Srivastava-Owa operators.

scholarly journals The generalized Gegenbauer-Humberts wavelet for solving fractional differential equations

2020 ◽  
Vol 24 (Suppl. 1) ◽  
pp. 107-118
Author(s):  
Jumana Alkhalissi ◽  
Ibrahim Emiroglu ◽  
Aydin Secer ◽  
Mustafa Bayram
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Fractional Differential Equation ◽  
Fractional Differential Equations ◽  
Operational Matrix ◽  
New Method ◽  
Algebraic Equations ◽  
Non Linear ◽  
Fractional Differential ◽  
Operational Matrix Of Integration

In this paper we present a new method of wavelets, based on generalized Gegen?bauer-Humberts polynomials, named generalized Gegenbauer-Humberts wave?lets. The operational matrix of integration are derived. By using the proposed method converted linear and non-linear fractional differential equation a system of algebraic equations. In addition, discussed some examples to explain the efficiency and accuracy of the presented method.

scholarly journals The generalized Gegenbauer-Humberts wavelet for solving fractional differential equations

2020 ◽  
Vol 24 (Suppl. 1) ◽  
pp. 107-118
Author(s):  
Jumana Alkhalissi ◽  
Ibrahim Emiroglu ◽  
Aydin Secer ◽  
Mustafa Bayram
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Fractional Differential Equation ◽  
Fractional Differential Equations ◽  
Operational Matrix ◽  
New Method ◽  
Algebraic Equations ◽  
Non Linear ◽  
Fractional Differential ◽  
Operational Matrix Of Integration

In this paper we present a new method of wavelets, based on generalized Gegen?bauer-Humberts polynomials, named generalized Gegenbauer-Humberts wave?lets. The operational matrix of integration are derived. By using the proposed method converted linear and non-linear fractional differential equation a system of algebraic equations. In addition, discussed some examples to explain the efficiency and accuracy of the presented method.

scholarly journals Solution of Multi-order Fractional Differential Equation Based on Conformable Derivative by Shifted Legendre Polynomial

2021 ◽  
Vol 5 (2) ◽  
pp. 64-68
Author(s):  
Salim S. Mahmood ◽  
Kamaran J. Hamad ◽  
‎Milad A. Kareem ◽  
Asrin F. Shex
Keyword(s):  
Differential Equation ◽  
Approximate Solution ◽  
Linear Equation ◽  
Fractional Differential Equation ◽  
Legendre Polynomial ◽  
Conformable Derivative ◽  
Approximation Solution ◽  
Non Linear Equation ◽  
Non Linear ◽  
Fractional Differential

The aim of this article is the way for finding approximation solution of multi-order fractional differential equation with conformable sense with use approximated function by shifted Legendre polynomial, the method is easy and powerful for get our results of the linear and non-linear equation, the background idea behind this method is finding system of algebra after achieving messing variable is that mean obtain approximate solution, a few examples illustrates for presented how much our method is capable.

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.

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