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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:
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
Descripción
Sumario: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.