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

Boundary value problems

Dumitru I Baleanu¹  Ioannis K Dassios² 

[1] Department of Mathematics and Computer Sciences, Cankaya University, Ankara, Turkey;School of Mathematics and Maxwell Institute, The University of Edinburgh, Edinburgh, United Kingdom

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

DOI  :  10.1186/1687-2770-2013-148

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

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.

【 授权许可】

CC BY