Radial symmetry for logarithmic Choquard equation involving a generalized tempered fractional <inline-formula><tex-math id="M1">$ p $</tex-math></inline-formula>-Laplacian

In this paper, we investigate radial symmetry and monotonicity of positive solutions to a logarithmic Choquard equation involving a generalized nonlinear tempered fractional \begin{document}$ p $\end{document} -Laplacian operator by applying the direct method of moving planes. We first introduce a new kind of tempered fractional \begin{document}$ p $\end{document} -Laplacian \begin{document}$ (-\Delta-\lambda_{f})_{p}^{s} $\end{document} based on tempered fractional Laplacian \begin{document}$ (\Delta+\lambda)^{\beta/2} $\end{document} , which was originally defined in [ 3 ] by Deng et.al [Boundary problems for the fractional and tempered fractional operators, Multiscale Model. Simul., 16(1)(2018), 125-149]. Then we discuss the decay of solutions at infinity and narrow region principle, which play a key role in obtaining the main result by the process of moving planes.