# Sensitivity of a nonlinear ordinary BVP with fractional Dirichlet-Laplace operator

## TL;DR

This paper establishes the continuous differentiability of solutions to a nonlinear fractional elliptic boundary value problem with respect to functional parameters, using a global implicit function theorem.

## Contribution

It introduces a novel sensitivity analysis framework for nonlinear fractional elliptic systems with Dirichlet boundary conditions.

## Key findings

- Existence and uniqueness of solutions for all functional parameters.
- Continuous differentiability of solutions with respect to parameters.
- Application of a global implicit function theorem to fractional elliptic problems.

## Abstract

In the paper, we derive a sensitivity result for a nonlinear fractional ordinary elliptic system on a bounded interval with Dirichlet boundary conditions. More precisely, using a global implicit function theorem, we show that, for any functional parameter, there exists a unique solution to such a problem and dependence of solutions on functional parameters is continuously differentiable.