Existence of a Unique Solution to a Fractional Partial Differential Equation and Its Continuous Dependence on Parameters

In the present paper we give conditions under which there exists a unique weak solution for a nonlocal equation driven by the integrodifferential operator of fractional Laplacian type. We argue for the optimality of some assumptions. Some Lyapunov-type inequalities are given. We also study the conti...

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Detalles Bibliográficos
Autor principal: Stegliński, Robert
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2021
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8303143/
https://www.ncbi.nlm.nih.gov/pubmed/34356392
http://dx.doi.org/10.3390/e23070851
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author Stegliński, Robert
author_facet Stegliński, Robert
author_sort Stegliński, Robert
collection PubMed
description In the present paper we give conditions under which there exists a unique weak solution for a nonlocal equation driven by the integrodifferential operator of fractional Laplacian type. We argue for the optimality of some assumptions. Some Lyapunov-type inequalities are given. We also study the continuous dependence of the solution on parameters. In proofs we use monotonicity and variational methods.
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spelling pubmed-83031432021-07-25 Existence of a Unique Solution to a Fractional Partial Differential Equation and Its Continuous Dependence on Parameters Stegliński, Robert Entropy (Basel) Article In the present paper we give conditions under which there exists a unique weak solution for a nonlocal equation driven by the integrodifferential operator of fractional Laplacian type. We argue for the optimality of some assumptions. Some Lyapunov-type inequalities are given. We also study the continuous dependence of the solution on parameters. In proofs we use monotonicity and variational methods. MDPI 2021-07-01 /pmc/articles/PMC8303143/ /pubmed/34356392 http://dx.doi.org/10.3390/e23070851 Text en © 2021 by the author. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Stegliński, Robert
Existence of a Unique Solution to a Fractional Partial Differential Equation and Its Continuous Dependence on Parameters
title Existence of a Unique Solution to a Fractional Partial Differential Equation and Its Continuous Dependence on Parameters
title_full Existence of a Unique Solution to a Fractional Partial Differential Equation and Its Continuous Dependence on Parameters
title_fullStr Existence of a Unique Solution to a Fractional Partial Differential Equation and Its Continuous Dependence on Parameters
title_full_unstemmed Existence of a Unique Solution to a Fractional Partial Differential Equation and Its Continuous Dependence on Parameters
title_short Existence of a Unique Solution to a Fractional Partial Differential Equation and Its Continuous Dependence on Parameters
title_sort existence of a unique solution to a fractional partial differential equation and its continuous dependence on parameters
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8303143/
https://www.ncbi.nlm.nih.gov/pubmed/34356392
http://dx.doi.org/10.3390/e23070851
work_keys_str_mv AT steglinskirobert existenceofauniquesolutiontoafractionalpartialdifferentialequationanditscontinuousdependenceonparameters

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