Approximation approach to the fractional BVP with the Dirichlet type boundary conditions

TL;DR

This paper develops a numerical-analytic method to approximate solutions of fractional differential boundary value problems with Dirichlet conditions, proving convergence and uniqueness, and validating results with an example.

Contribution

It introduces a new approximation technique for fractional BVPs with Dirichlet conditions, including convergence proof and solution existence criteria.

Findings

Sequence of approximations converges uniformly to the unique solution.

Necessary and sufficient conditions for solution existence are established.

Method is validated through a model example.

Abstract

We use a numerical-analytic technique to construct a sequence of successive approximations to the solution of a system of fractional differential equations, subject to Dirichlet boundary conditions. We prove the uniform convergence of the sequence of approximations to a limit function, which is the unique solution to the boundary value problem under consideration, and give necessary and sufficient conditions for the existence of solutions. The obtained theoretical results are confirmed by a model example.