Dassios, Ioannis K.

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Dassios, Ioannis K.
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Dassios, Ioannis K.

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  • Publication
    Geometric relation between two different types of initial conditions of singular systems of fractional nabla difference equations
    (Wiley Online Library, 2017-11-30)
    Dassios, Ioannis K. 
    In this article, we study the geometric relation between two different types of initial conditions (IC) of a class of singular linear systems of fractional nabla difference equations whose coefficients are constant matrices. For these kinds of systems, we analyze how inconsistent and consistent IC are related to the column vector space of the finite and the infinite eigenvalues of the pencil of the system and analyze the geometric connection between these two different types of IC. Numerical examples are given to justify the results.
      323Scopus© Citations 18
  • Publication
    Caputo and related fractional derivatives in singular systems
    (Elsevier, 2018-11-15)
    Dassios, Ioannis K. 
    ;
    Baleanu, Dumitru 
    By using 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, firstly we focus on singular linear systems of fractional differential equations with constant coefficients that can be non-square matrices, or square & singular. We study existence of solutions and provide formulas for the case that there do exist solutions. Then, we study the existence of unique solution for given initial conditions. Several numerical examples are given to justify our theory.
      350Scopus© Citations 47
  • Publication
    Optimal solutions for singular linear systems of Caputo fractional differential equations
    (Wiley, 2018-12-06)
    Dassios, Ioannis K. 
    ;
    Baleanu, Dumitru 
    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.
      635Scopus© Citations 24