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

On a class of Kirchhoff-Choquard equations involving variable-order  fractional $p(\cdot)-$ Laplacian and without Ambrosetti-Rabinowitz type  condition