  In this article we study the existence of weak solution, existence of ground
state solution using Nehari manifold and existence of infinitely many solutions
using Fountain theorem and Dual fountain theorem for a class of doubly nonlocal
Kirchhoff-Choquard type equations involving the variable-order fractional
$p(\cdot)-$ Laplacian operator. Here the nonlinearity does not satisfy the well
known Ambrosetti-Rabinowitz type condition.
