Existence and Monotone Iterative Approximation of Solutions for Neutral Differential Equations with Generalized Fractional Derivatives

We study the existence and monotone iterative approximation of mild solutions of fractional-order neutral differential equations involving a generalized fractional derivative of order 0 < alpha < 1 which can be reduced to Riemann-Liouville or Hadamard fractional derivatives. The existence of mild solutions is obtained via fixed point techniques in a partially ordered space. The approach is constructive and can be applied numerically. In particular, we construct a monotone sequence of functions converging to a solution which is illustrated by a numerical example.

Automated summary

This paper studies the existence and monotone iterative approximation of mild solutions of fractional-order neutral differential equations involving a generalized fractional derivative. The existence of mild solutions is obtained via fixed point techniques in a partially ordered space. The approach is constructive and can be applied numerically, and an example is provided to demonstrate the convergence of a monotone sequence of functions to a solution.