Initial value problem for fractional Volterra integrodifferential pseudo-parabolic equations

In this paper, we investigate a initial value problem for the Caputo time-fractional pseudo-parabolic equations with fractional Laplace operator of order 0 < ν ≤ 1 and nonlinear memory source term. For 1, will be considered on bounded domain ℝ d . By some Sobolev embeddings properties Mittag-Leffler function, give results existence uniqueness mild solution (1.1) below. When = introduce L p − q estimates, based them derive global in whole space