A Study of Nonlinear Boundary Value Problem

*Noureddine Bouteraa and Habib Djourdem*

## **Abstract**

In this chapter, firstly we apply the iterative method to establish the existence of the positive solution for a type of nonlinear singular higher-order fractional differential equation with fractional multi-point boundary conditions. Explicit iterative sequences are given to approximate the solutions and the error estimations are also given. Secondly, we cover the multi-valued case of our problem. We investigate it for nonconvex compact valued multifunctions via a fixed point theorem for multivalued maps due to Covitz and Nadler. Two illustrative examples are presented at the end to illustrate the validity of our results.

**Keywords:** Positive solution, Uniqueness, Iterative sequence, Green's function, Fractional differential equation and inclusion, Existence, Nonlocal boundary value problem, Fixed point theorem
