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This paper deals with Strauss and Lions-type theorems for fractional Sobolevspaces with variable exponent $W^{s,p(.),\tilde{p}(.,.)}(\Omega)$, when $p$ and$\tilde{p}$ satisfies some conditions. As application, we study the existenceof solutions for a class of Kirchhoff-Choquard problem in $\mathbb{R}^N$.

Strauss and Lions type theorems for the fractional Sobolev spaces with variable exponent and applications to nonlocal Kirchhoff-Choquard problem