<p>This paper investigates fractional order pantograph mixed Volterra-Fredholm delay-integro-differential equations using a new numerical approach that leverages Bernoulli polynomials and the Gauss quadrature formula. The process begins with converting the original equation into an equivalent Volterra integral equation. We then establish the existence and uniqueness of this equivalent Volterra integral equation using Gronwall inequality, which in turn ensures the existence and uniqueness of the solution of the original equation. Following this, the transformed equation is efficiently solved using Bernoulli polynomials in conjunction with the Gauss quadrature formula. Additionally, the error analysis for the proposed numerical method is presented. Lastly, several numerical experiments are provided to illustrate the high accuracy and good approximation of the proposed method.</p>