It is important that we increase our ability for studying of complicate fractional integro-differential equation. In this paper, we investigates the existence of solutions for a pointwise defined multi-singular fractional differential equation under some integral boundary conditions. We provide an example to illustrate our main result. MSC: Primary 34A08; secondary 34A60Keywords: Multi-singularity; Pointwise defined fractional equation; The Caputo derivation 1 0 x(t) dt = m and x (0) = x (3) (0) = · · · = x (n-1) (0) = 0, where 0 < t < 1, m is a real number, n ≥ 2, α ∈ (n -1, n), 0 < β < 1, D α and