Duality of singular linear systems of fractional nabla difference equations

22Citations
Citations of this article
5Readers
Mendeley users who have this article in their library.

Abstract

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.

Cite

CITATION STYLE

APA

Dassios, I. K., & Baleanu, D. I. (2015). Duality of singular linear systems of fractional nabla difference equations. Applied Mathematical Modelling, 39(14), 4180–4195. https://doi.org/10.1016/j.apm.2014.12.039

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free