Paper Info
Title
Computational Methods for Parameter Identification in 2D Fractional System with Riemann-Liouville Derivative
Abstract
In recent times, many different types of systems have been based on fractional derivatives. Thanks to this type of derivatives, it is possible to model certain phenomena in a more precise and desirable way. This article presents a system consisting of a two-dimensional fractional differential equation with the Riemann-Liouville derivative with a numerical algorithm for its solution. The presented algorithm uses the alternating direction implicit method (ADIM). Further, the algorithm for solving the inverse problem consisting of the determination of unknown parameters of the model is also described. For this purpose, the objective function was minimized using the ant algorithm and the Hooke-Jeeves method. Inverse problems with fractional derivatives are important in many engineering applications, such as modeling the phenomenon of anomalous diffusion, designing electrical circuits with a supercapacitor, and application of fractional-order control theory. This paper presents a numerical example illustrating the effectiveness and accuracy of the described methods. The introduction of the example made possible a comparison of the methods of searching for the minimum of the objective function. The presented algorithms can be used as a tool for parameter training in artificial neural networks.
Year
DOI
Venue
2022
10.3390/s22093153
SENSORS
Keywords
DocType
Volume
inverse problem, fractional system, fractional derivative, parameter identification, fractional differential equation, heuristic algorithm, computational methods
Journal
22
Issue
ISSN
Citations 
9
1424-8220
0
PageRank 
References 
Authors
0.34
2
5
Name
Order
Citations
PageRank
r brociek1103.35
Agata Wajda200.34
Grazia Lo Sciuto300.34
Damian Słota400.34
Giacomo Capizzi500.34