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A unified fixed point approach to study the existence of solutions for a class of fractional boundary value problems arising in a chemical graph theory
A theory of chemical graphs is a part of mathematical chemistry concerned with the effects of connectedness in chemical graphs. Several researchers have studied the solutions of fractional differential equations using the concept of star graphs. They employed star graphs because their technique requ...
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Formato: | Online Artículo Texto |
Lenguaje: | English |
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Public Library of Science
2022
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Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9374263/ https://www.ncbi.nlm.nih.gov/pubmed/35960746 http://dx.doi.org/10.1371/journal.pone.0270148 |
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author | Sintunavarat, Wutiphol Turab, Ali |
author_facet | Sintunavarat, Wutiphol Turab, Ali |
author_sort | Sintunavarat, Wutiphol |
collection | PubMed |
description | A theory of chemical graphs is a part of mathematical chemistry concerned with the effects of connectedness in chemical graphs. Several researchers have studied the solutions of fractional differential equations using the concept of star graphs. They employed star graphs because their technique requires a central node with links to adjacent vertices but no edges between nodes. The purpose of this paper is to extend the method’s range by introducing the concept of an octane graph, which is an essential organic compound having the formula C(8)H(18). In this manner, we analyze a graph with vertices annotated by 0 or 1, which is influenced by the structure of the chemical substance octane, and formulate a fractional boundary value problem on each of the graph’s edges. We use the Schaefer and Krasnoselskii fixed point theorems to investigate the existence of solutions to the presented boundary value problems in the framework of the Caputo fractional derivative. Finally, two examples are provided to highlight the importance of our results in this area of study. |
format | Online Article Text |
id | pubmed-9374263 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2022 |
publisher | Public Library of Science |
record_format | MEDLINE/PubMed |
spelling | pubmed-93742632022-08-13 A unified fixed point approach to study the existence of solutions for a class of fractional boundary value problems arising in a chemical graph theory Sintunavarat, Wutiphol Turab, Ali PLoS One Research Article A theory of chemical graphs is a part of mathematical chemistry concerned with the effects of connectedness in chemical graphs. Several researchers have studied the solutions of fractional differential equations using the concept of star graphs. They employed star graphs because their technique requires a central node with links to adjacent vertices but no edges between nodes. The purpose of this paper is to extend the method’s range by introducing the concept of an octane graph, which is an essential organic compound having the formula C(8)H(18). In this manner, we analyze a graph with vertices annotated by 0 or 1, which is influenced by the structure of the chemical substance octane, and formulate a fractional boundary value problem on each of the graph’s edges. We use the Schaefer and Krasnoselskii fixed point theorems to investigate the existence of solutions to the presented boundary value problems in the framework of the Caputo fractional derivative. Finally, two examples are provided to highlight the importance of our results in this area of study. Public Library of Science 2022-08-12 /pmc/articles/PMC9374263/ /pubmed/35960746 http://dx.doi.org/10.1371/journal.pone.0270148 Text en © 2022 Sintunavarat, Turab https://creativecommons.org/licenses/by/4.0/This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/) , which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. |
spellingShingle | Research Article Sintunavarat, Wutiphol Turab, Ali A unified fixed point approach to study the existence of solutions for a class of fractional boundary value problems arising in a chemical graph theory |
title | A unified fixed point approach to study the existence of solutions for a class of fractional boundary value problems arising in a chemical graph theory |
title_full | A unified fixed point approach to study the existence of solutions for a class of fractional boundary value problems arising in a chemical graph theory |
title_fullStr | A unified fixed point approach to study the existence of solutions for a class of fractional boundary value problems arising in a chemical graph theory |
title_full_unstemmed | A unified fixed point approach to study the existence of solutions for a class of fractional boundary value problems arising in a chemical graph theory |
title_short | A unified fixed point approach to study the existence of solutions for a class of fractional boundary value problems arising in a chemical graph theory |
title_sort | unified fixed point approach to study the existence of solutions for a class of fractional boundary value problems arising in a chemical graph theory |
topic | Research Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9374263/ https://www.ncbi.nlm.nih.gov/pubmed/35960746 http://dx.doi.org/10.1371/journal.pone.0270148 |
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