Approximation Approach to the Fractional BVP with the Dirichlet Type Boundary Conditions

Journal article (2022)

Authors

K. Marynets Mathematical Physics - EEMCS
D.H. Pantova Mathematical Physics - EEMCS
Research Group
Mathematical Physics (EEMCS) (TU Delft)
Copyright: © 2022 K. Marynets, D.H. Pantova
DOI: https://doi.org/10.1007/s12591-022-00613-y
Approximation of solutions Brouwer degree Dirichlet boundary conditions Fractional differential equations
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Published Date

2022

Language

English

Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Mathematical Physics

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.