Analysis of impulsive fractional functional differential equations (PhD)

Abstract

Impulsive fractional functional differential equations are analyzed and applied to the fields like ecological system, control theory and neural network. Impulsive differential equations, fractional differential equations and functional differential equations, first discussed, then the combination of all these three, as impulsive fractional functional differential equations, are analyzed. Such a generalized differential equation can suitably model, the evolutionary systems that exhibit delay, impulsive effect and anomalous characteristics. After formulating initial value problems for these systems and defining corresponding solution, several theorems on dynamical analysis of solutions of these problems are established and analyzed. In the dynamical analysis, existence, uniqueness, stability, permanence, persistence, numerical simulation of solutions are carried out. Fixed point methods, ð€€€ resolvent family of bounded linear operators, Lyapunov function, Razumikhin technique and fractional Adams-Bashforth-Moulton numerical techniques are main tools applied in the analysis of our problems. Finally, several examples and applications are given from motivation point of view.