scholarly journals Research on nature-inspired metaheuristics for optimal control of fractional differential equation

Authorea ◽  
2020 ◽  
Author(s):  
Asyieh Ebrahimzadeh ◽  
Raheleh Khanduzi ◽  
Samaneh Panjeh Ali Beik
Keyword(s):  
Differential Equation ◽  
Optimal Control ◽  
Fractional Differential Equation ◽  
Fractional Differential ◽  
Nature Inspired Metaheuristics

Optimal Control Problem for a Degenerate Fractional Differential Equation

2021 ◽  
Vol 42 (6) ◽  
pp. 1239-1247
Author(s):  
R. A. Bandaliyev ◽  
I. G. Mamedov ◽  
A. B. Abdullayeva ◽  
K. H. Safarova
Keyword(s):  
Differential Equation ◽  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Fractional Differential Equation ◽  
Fractional Differential

scholarly journals On controllability for a nondensely defined fractional differential equation with a deviated argument

2019 ◽  
Vol 13 (4) ◽  
pp. 407-413
Author(s):  
A. Raheem ◽  
M. Kumar
Keyword(s):  
Differential Equation ◽  
Optimal Control ◽  
Fixed Point ◽  
Fractional Differential Equation ◽  
Measure Of Noncompactness ◽  
Cosine Family ◽  
Abstract Result ◽  
Deviated Argument ◽  
Approximately Controllable ◽  
Fractional Differential

Abstract This article deals with a fractional differential equation with a deviated argument defined on a nondense set. A fixed-point theorem and the concept of measure of noncompactness are used to prove the existence of a mild solution. Furthermore, by using the compactness of associated cosine family, we proved that system is approximately controllable and obtains an optimal control which minimizes the performance index. To illustrate the abstract result, we included an example.

scholarly journals Solution of Some Types for Composition Fractional Order Differential Equations Corresponding to Optimal Control Problems

2018 ◽  
Vol 2018 ◽  
pp. 1-12
Author(s):  
Sameer Qasim Hasan ◽  
Moataz Abbas Holel
Keyword(s):  
Differential Equation ◽  
Optimal Control ◽  
Fractional Differential Equation ◽  
Fractional Order ◽  
Optimal Control Problems ◽  
Chebyshev Approximation ◽  
Approximate Solutions ◽  
Control Problems ◽  
Fractional Differential ◽  
Working Method

The approximate solution for solving a class of composition fractional order optimal control problems (FOCPs) is suggested and studied in detail. However, the properties of Caputo and Riemann-Liouville derivatives are also given with complete details on Chebyshev approximation function to approximate the solution of fractional differential equation with different approach. Also, the relation between Caputo and Riemann-Liouville of fractional derivative took a big role for simplifying the fractional differential equation that represents the constraints of optimal control problems. The approximate solutions are defined on interval [0,1] and are compared with the exact solution of order one which is an important condition to support the working method. Finally, illustrative examples are included to confirm the efficiency and accuracy of the proposed method.

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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