Matematik Bölümü Yayın Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413

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Author: search.filters.author.Baleanu, Dumitru I.Subject: search.filters.subject.Fractional Calculus

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  • Article
    Citation - WoS: 20
    Citation - Scopus: 36
    On a Singular System of Fractional Nabla Difference Equations With Boundary Conditions
    (Springeropen, 2013) Baleanu, Dumitru I.; Dassios, Ioannis K.
    In this article, we study a boundary value problem of a class of linear singular systems of fractional nabla difference equations whose coefficients are constant matrices. By taking into consideration the cases that the matrices are square with the leading coefficient matrix singular, square with an identically zero matrix pencil and non-square, we provide necessary and sufficient conditions for the existence and uniqueness of solutions. More analytically, we study the conditions under which the boundary value problem has a unique solution, infinite solutions and no solutions. Furthermore, we provide a formula for the case of the unique solution. Finally, numerical examples are given to justify our theory.
  • Article
    Citation - WoS: 30
    Citation - Scopus: 46
    On Non-Homogeneous Singular Systems of Fractional Nabla Difference Equations
    (Elsevier Science inc, 2014) Baleanu, Dumitru I.; Kalogeropoulos, Grigoris I.; Dassios, Ioannis K.
    In this article we study the initial value problem of a class of non-homogeneous singular systems of fractional nabla difference equations whose coefficients are constant matrices. By taking into consideration the cases that the matrices are square with the leading coefficient singular, non-square and square with a matrix pencil which has an identically zero determinant, we provide necessary and sufficient conditions for the existence and uniqueness of solutions. More analytically we study the conditions under which the system has unique, infinite and no solutions. Furthermore, we provide a formula for the case of the unique solution. Finally, numerical examples are given to justify our theory. Crown Copyright (C) 2013 Published by Elsevier Inc. All rights reserved.