On the singular elliptic problem involving the variable order fractional Musielak $g_{x,y}$-Laplacian

TL;DR

This paper studies the existence of positive solutions to a nonlocal singular elliptic problem involving a variable order fractional Musielak-Laplacian, using variational methods in specialized function spaces.

Contribution

It introduces a framework for analyzing singular elliptic problems with variable order fractional Musielak-Laplacian using variational techniques.

Findings

Existence of positive weak solutions established.

Application of variational and critical point theory methods.

Analysis conducted in fractional Musielak-Sobolev spaces.

Abstract

In this paper, we investigate the existence of positive weak solutions to a nonlocal singular elliptic problem under Dirichlet boundary condition. Problem is settled in fractional Musielak-Sobolev spaces with variable order. The main tool is variational approach, however, various auxiliary tools from the theory of nonlinear functional analysis, convex analysis and critical point theory are also applied.