Optimal solutions for singular linear systems of Caputo fractional differential equations

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Title: Optimal solutions for singular linear systems of Caputo fractional differential equations
Authors: Dassios, Ioannis K.
Baleanu, Dumitru
Permanent link: http://hdl.handle.net/10197/10553
Date: 6-Dec-2018
Online since: 2019-05-21T07:34:12Z
Abstract: In this article, we focus on a class of singular linear systems of fractional differential equations with given nonconsistent initial conditions (IC). Because the nonconsistency of the IC can not lead to a unique solution for the singular system, we use two optimization techniques to provide an optimal solution for the system. We use two optimization techniques to provide the optimal solution for the system because a unique solution for the singular system cannot be obtained due to the non-consistency of the IC. These two optimization techniques involve perturbations to the non-consistent IC, specifically, an l2 perturbation (which seeks an optimal solution for the system in terms of least squares), and a second-order optimization technique at an l1 minimum perturbation, (which includes an appropriate smoothing). Numerical examples are given to justify our theory. We use the Caputo (C) fractional derivative and two recently defined alternative versions of this derivative, the Caputo-Fabrizio (CF) and the Atangana-Baleanu (AB) fractional derivative.
Funding Details: Science Foundation Ireland
Type of material: Journal Article
Publisher: Wiley Online Library
Journal: Mathematical Methods in the Applied Sciences
Start page: 1
End page: 13
Copyright (published version): 2018 John Wiley & Sons, Ltd.
Keywords: Singular systemOptimal solutionsFractional derivativeCaputoInitial conditions
DOI: 10.1002/mma.5410
Language: en
Status of Item: Peer reviewed
Appears in Collections:Electrical and Electronic Engineering Research Collection

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