Open Access Research

On a singular system of fractional nabla difference equations with boundary conditions

Ioannis K Dassios1* and Dumitru I Baleanu234

Author Affiliations

1 School of Mathematics and Maxwell Institute, The University of Edinburgh, Mayfield Road, Edinburgh, EH9 3JZ, United Kingdom

2 Department of Mathematics and Computer Sciences, Cankaya University, Ankara, Turkey

3 Institute of Space Sciences, Magurele, Bucharest, Romania

4 Department of Chemical and Materials Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah, Saudi Arabia

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Boundary Value Problems 2013, 2013:148  doi:10.1186/1687-2770-2013-148

Published: 19 June 2013

Abstract

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.

Keywords:
boundary conditions; singular systems; fractional calculus; nabla operator; difference equations; linear; discrete time system