Browsing by Author "Baleanu, Dumitru I."

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Duality of singular linear systems of fractional nabla difference equations
(Elsevier Science inc, 2015) Dassios, Ioannis K.; Baleanu, Dumitru; Baleanu, Dumitru I.
The main objective of this article is to provide a link between the solutions of an initial value problem of a linear singular system of fractional nabla difference equations, its proper dual system and its transposed dual system. By taking into consideration the case that the coefficients are square constant matrices with the leading coefficient singular, we study the prime system and by using the invariants of its pencil we give necessary and sufficient conditions for existence and uniqueness of solutions. After we prove that by using the pencil of the prime system we can study the existence and uniqueness of solutions of the proper dual system and the transposed dual system. Moreover their solutions, when they exist, can be explicitly represented without resorting to further processes of computations for each one separately. Finally, numerical examples are given based on a singular fractional nabla real dynamical system to justify our theory. (C) 2014 Elsevier Inc. All rights reserved.
On A Singular System of Fractional Nabla Difference Equations With Boundary Conditions
(Springeropen, 2013) Dassios, Ioannis K.; Baleanu, Dumitru; Baleanu, Dumitru I.; 56389
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.
On Non-Homogeneous Singular Systems of Fractional Nabla Difference Equations
(Elsevier Science inc, 2014) Dassios, Ioannis K.; Baleanu, Dumitru; Baleanu, Dumitru I.; Kalogeropoulos, Grigoris I.; 56389
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.