Fractional Musielak spaces: study of nonlocal elliptic problem with Choquard-logarithmic nonlinearity

In this study, we thoroughly examine a specific type of complex mathematical problems involving a fractional psi(kappa,y)(& sdot;)-Laplacian operator and a Choquard-logarithmic nonlinearity, combined with a real parameter, known as non-homogeneous elliptic problems. Our approach involves setting-specific conditions for the Choquard nonlinearities and the continuous function psi(kappa,y). This allows us to successfully identify multiple solutions to these problems. Our analysis is conducted in the area of fractional Musielak spaces. We rely heavily on the mountain pass theorem and Ekeland's variational principle, as well as the Hardy-Littlewood-Sobolev inequality, which is essential for supporting the theoretical basis of our research.