In this paper, the new delay-dependent admissibility of delay neutral singular systems with fractional order derivative is discussed. We define the new admissibility conditions in terms of matrix inequalities by using model transformation, useful lemmas, zero equations, Lyapunov-Krasovskii functionals and other well-known inequalities. Then, we prove the admissibility conditions of the considered fractional delay neutral singular systems. Also, we give some numerical illustrations with the help of MATLAB-Simulink to verify and justify these theoretically proven claims.