On non-homogeneous singular systems of fractional nabla difference equations

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• 作者：Ioannis K. Dassios ; Dumitru I. Baleanu ; Grigoris I. Kalogeropoulos
• 关键词：Singular systems ; Fractional calculus ; Nabla operator ; Difference equations ; Linear ; Discrete time system
• 刊名：Applied Mathematics and Computation
• 出版年：15 January, 2014
• 年：2014
• 卷：227
• 期：Complete
• 页码：112-131
• 全文大小：574 K

文摘

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.