Équations linéaires aux différences q-non uniformes du second ordre

Abstract

This work is devoted to the study of second-order linear equations with q-nonuniform differences, which generalize classical difference equations and are used in the modeling of discrete dynamical systems. After a review of the fundamental concepts of q-nonuniform difference calculus, including differentiation and integration, this thesis presents a study of second-order linear q-nonuniform difference equations. The main analysis focuses on second-order linear q-nonuniform difference equations. Solvability conditions are examined for both constant and variable coefficients, and then the orthogonality and controllability properties of the solutions are studied. The results obtained lead to the construction of the controllability matrix of the system under study and provide a better understanding of the structure and behavior of these equations, while highlighting their significance in applied mathematics.