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Article

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

Institute of Mathematics, Lodz University of Technology, Wólczańska 215, 90-924 Lodz, Poland
Academic Editors: Ravi P. Agarwal and Maria Alessandra Ragusa
Received: 6 June 2021 / Revised: 28 June 2021 / Accepted: 28 June 2021 / Published: 1 July 2021
(This article belongs to the Special Issue Nonlinear Dynamics and Analysis)
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. View Full-Text
Keywords: monotone operator; unique solution; Lyapunov-type inequalities; dependence on parameters monotone operator; unique solution; Lyapunov-type inequalities; dependence on parameters
MDPI and ACS Style

Stegliński, R. Existence of a Unique Solution to a Fractional Partial Differential Equation and Its Continuous Dependence on Parameters. Entropy 2021, 23, 851. https://0-doi-org.brum.beds.ac.uk/10.3390/e23070851

AMA Style

Stegliński R. Existence of a Unique Solution to a Fractional Partial Differential Equation and Its Continuous Dependence on Parameters. Entropy. 2021; 23(7):851. https://0-doi-org.brum.beds.ac.uk/10.3390/e23070851

Chicago/Turabian Style

Stegliński, Robert. 2021. "Existence of a Unique Solution to a Fractional Partial Differential Equation and Its Continuous Dependence on Parameters" Entropy 23, no. 7: 851. https://0-doi-org.brum.beds.ac.uk/10.3390/e23070851

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