Existence of solutions to the generalized periodic fractional boundary value problem

Michal Fečkan; Kateryna Marynets; Jin Rong Wang

doi:10.1002/mma.9097

Existence of solutions to the generalized periodic fractional boundary value problem

Michal Fečkan, Kateryna Marynets^*, Jin Rong Wang

^*Corresponding author for this work

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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.

Original language	English
Pages (from-to)	11971-11982
Number of pages	12
Journal	Mathematical Methods in the Applied Sciences
Volume	46
Issue number	11
DOIs	https://doi.org/10.1002/mma.9097
Publication status	Published - 2023

Keywords

existence of solutions
fractional boundary value problem
periodic boundary conditions
topological index

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10.1002/mma.9097

Math Methods in App Sciences - 2023 - Fe kan - Existence of solutions to the generalized periodic fractional boundary valueFinal published version, 403 KBLicence: CC BY

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title = "Existence of solutions to the generalized periodic fractional boundary value problem",

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.",

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AU - Marynets, Kateryna

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AB - 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.

KW - existence of solutions

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KW - periodic boundary conditions

KW - topological index

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JO - Mathematical Methods in the Applied Sciences

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Existence of solutions to the generalized periodic fractional boundary value problem

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