Monotone Iterative Technique for Impulsive Riemann-Liouville Fractional Differential Equations

Abstract

Monotone iterative technique coupled with the method of lower and upper solutions is employed for studying the existence and uniqueness of mild solution to an impulsive Riemann-Liouville fractional differential equation. The results are obtained using the concept of measure of noncompactness, semigroup theory and generalized Gronwall inequality for fractional differential equations. At last, an example is given to illustrate the applications of the main results.