Weak and viscosity solutions for non-homogeneous fractional equations in Orlicz spaces

TL;DR

This paper establishes the equivalence between weak and viscosity solutions for non-homogeneous fractional equations within Orlicz spaces, advancing the understanding of solutions in complex functional frameworks.

Contribution

It introduces a novel equivalence result for weak and viscosity solutions in the context of non-homogeneous fractional equations in Orlicz spaces.

Findings

Proved the equivalence between weak and viscosity solutions.

Extended the fractional calculus framework to Orlicz spaces.

Provided new tools for analyzing non-homogeneous fractional PDEs.

Abstract

In this paper, we consider non-homogeneous fractional equations in Orlicz spaces, with a source depending on the spatial variable, the unknown function, and its fractional gradient. The latter is adapted to the Orlicz framework. The main contribution of the article is to establish the equivalence between weak and viscosity solutions for such equations.