MONOTONE-ITERATIVE TECHNIQUES FOR MILD SOLUTIONS OF THE INITIAL VALUE PROBLEM FOR CAPUTO FRACTIONAL DIFFERENTIAL EQUATIONS WITH NON-INSTANTANEOUS IMPULSES

摘要

The main aim of the paper is to suggest some algorithms to approximately solve the initial value problem for scalar nonlinear Caputo fractional differential equations with noninstantaneous impulses. The impulses start abruptly at some points and their action continue on given finite intervals. We study the case when the right hand side of the equations are monotonic functions. Several types of mild lower and mild upper solutions to the problem are defined and used in the algorithms. The convergence of the successive approximations is established. A generalization of the logistic equation is given to illustrate the results.