A study on existence and stability results for impulsive fractional differential equations

Abstract

newline This research investigates the mild solution and its uniqueness for fractional impulsive differential systems of the Sobolev type with fractional order nonlocal boundary conditions. The research reported in this thesis discusses the initial value problem for impulsive fractional differential equations on an infinite interval with the Hilfer type. In addition, the present work investigates the existence of mild solutions on an infinite interval, while the latter part discusses the existence and uniqueness of outcomes for sequential and#968; -Hilfer impulsive fractional differential equations with boundary conditions at multi-points. The existence and uniqueness of solutions are based on fixed point theorems, such as the Banach contraction mapping principle and the Schauder fixed point theorem. The Banach contraction mapping principle is used to prove the uniqueness results for fractional differential equations. In addition, the research studied the existence of a solution for the impulsive integrodifferential equations with the and#968; fractional derivative. Finally, the study proved the solution of Ulam-Hyers stability. Ultimately, a few examples are presented to elucidate the principal results