Existence of solutions to the generalized periodic fractional boundary value problem

Journal article (2023)

Authors

Michal Fečkan Comenius University, Mathematical Institute of Slovak Academy of Sciences
K. Marynets Mathematical Physics - EEMCS
J. Wang Guizhou University, Mechanical Engineering
Research Group
Mathematical Physics (EEMCS) (TU Delft)
Copyright: © 2023 Michal Fečkan, K. Marynets, J. Wang
DOI: https://doi.org/10.1002/mma.9097
Periodic boundary conditions Existence of solutions Fractional boundary value problem Topological index
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Published Date

2023

Language

English

Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Mathematical Physics

Abstract

We study a boundary value problem for a Caputo-type fractional differential equation subjected to periodic boundary conditions. For an auxiliary problem with the simplified right-hand side, we explicitly construct its unique solution. In addition, based on the theory of the topological index, we prove existence of at least one solution to the original problem.