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

Entropy (Basel). 2021 Jul 1;23(7):851. doi: 10.3390/e23070851.

Abstract

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.

Keywords: Lyapunov-type inequalities; dependence on parameters; monotone operator; unique solution.