Differential inclusion systems with fractional competing operator and multivalued fractional convection term

TL;DR

This paper proves the existence of solutions for complex fractional differential inclusion systems involving competing operators and convection terms, using Galerkin's method and advanced mathematical tools.

Contribution

It introduces a novel approach to establish solutions for fractional inclusion systems with competing operators and convection, expanding the theoretical framework.

Findings

Existence of solutions for the studied systems is confirmed.

The approach combines Galerkin's method with surjective results for multifunctions.

The results apply to systems with fractional elliptic operators and boundary conditions.

Abstract

In this work, the existence of solutions (in a suitable sense) to a family of inclusion systems involving fractional, possibly competing, elliptic operators, fractional convection, and homogeneous Dirichlet boundary conditions is established. The technical approach exploits Galerkin's method and a surjective results for multifunctions in finite dimensional spaces as well as approximating techniques.