Browsing by Author "Dassios, Ioannis"

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    Citation - WoS: 16
    Citation - Scopus: 18
    Fractional-Order Dynamical Model for Electricity Markets
    (Wiley, 2023) Kerci, Taulant; Baleanu, Dumitru; Milano, Federico; Dassios, Ioannis
    In this article, we use a generalized system of differential equations of fractional-order to incorporate memory into an electricity market model. By using this idea, essential information from the past, such as the behavior of market participants, namely, suppliers and consumers, can be used and have impact on future decisions. We construct the fractional-order dynamical model, study its solutions, and provide closed formulas of solutions. Finally, we provide an application by using the proposed formula of solutions as well as a numerical example which also compares the proposed model with a conventional, integer-order electricity market model. Results indicate that the inclusion of memory leads market participants to adopt a conservative behavior.
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    Article
    Citation - WoS: 35
    Citation - Scopus: 31
    Optimal Solutions for Singular Linear Systems of Caputo Fractional Differential Equations
    (Wiley, 2021) Baleanu, Dumitru; Dassios, Ioannis
    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 l(2) perturbation (which seeks an optimal solution for the system in terms of least squares), and a second-order optimization technique at an l(1) 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.