In this paper we study the existence and regularity results of normalized solutions to the following quasilinear elliptic Choquard equation with critical Sobolev exponent and mixed diffusion type operators: − ∆ p u +( − ∆ p ) s u = λ | u | p − 2 u + | u | p ∗ − 2 u + µ ( I α ∗ | u | q ) | u | q − 2 u in R N , ∫ R N | u | p dx = τ , where N≥3, τ>0, p 2 ( N + α N ) < q < p 2 ( N + α N − p ) , I α is the Riesz potential of order α∈(0 ,N), µ>0 is a parameter, ( − ∆ p ) s is the fractional p-laplacian operator, p ∗ = Np N − p is the critical Sobolev exponent and λ appears as a Lagrange multiplier.

In the present paper, we study a class of quasilinear Choquard equations involving N-Laplacian and the nonlinearity with the critical exponential growth. We discuss the existence of positive solutions of such equations.