Ulam type stability of non-instantaneous impulsive Riemann-Liouville fractional differential equations(changed lower bound of the fractional derivative)

Abstract

Recent modeling of real world phenomena give rise to fractional differential equations with non-instantaneous impulses. The main goal of the paper is to highlight basic points in introducing non-instantaneous impulses in Riemann-Liouville fractional differential equations. The case when the lower limit of the fractional derivative is changed at any point of stop acting the impulse is studied. It is studied the initial value problem when both the initial condition and the non-instantaneous impulsive conditions are in Riemann integral form. Generalized Ulam-Hyers-Rassias stability is defined and applied to study the existence of the solution. An example is illustrated the result.