Ulam Hyers and Lyapunov Stability for Some Classes of Fractional Differential Equations and Difference Equations

Abstract

Studying the behavior of a dynamical system and the dependency of its solution on the newlineinitial state or initial condition began in the late 1880s. Describing the dynamics of newlinedynamical systems as a function of time on the state space can generate a differential newlineequation. Thus, the theory of dynamical systems may be said to be a special and important topic in the theory of differential equations. It falls under the qualitative theory which is mainly concerned with properties which are not quantified. The study of qualitative theory leads to a better understanding of the dynamical systems.