Nonlocal fractional differential equations and applications

TL;DR

This paper investigates boundary value problems for nonlocal fractional elliptic equations in Banach spaces, establishing resolvent estimates, sectoriality, and regularity properties, with applications to anisotropic and system fractional differential equations.

Contribution

It provides new resolvent estimates, proves sectoriality and semigroup generation for nonlocal fractional elliptic operators, and extends maximal regularity results to nonlocal fractional parabolic equations.

Findings

Established uniform $L_p$-separability properties.

Proved the fractional elliptic operator is sectorial and generates an analytic semigroup.

Demonstrated maximal regularity for nonlocal fractional parabolic equations.

Abstract

Boundary value problems for nonlocal fractional elliptic equations with parameter in Banach spaces are studied. Uniform $L_p$-separability properties and sharp resolvent estimates are obtained for elliptic equations in terms of fractional derivatives. Particularly, it is proven that the fractional ellipitic operator generated by these equations is sectorial and also is a generator of an analytic semigroup. Moreover, maximal regularity properties of nonlocal fractional abstract parabolic equation are established. As an application, the nonlocal anisotropic fractional differential equations and the system of nonlocal fractional differential equations are studied.