‎This article presents a numerical method for addressing a category of nonlinear multi-term variable-order fractional derivative equations‎. ‎The approach relies on creating a Bernoulli operational matrix (BOM) for fractional variable-order derivatives‎. ‎This technique is utilized to address a category of these equations‎, ‎transforming the original problem into a system of algebraic equations amenable to numerical solutions‎. ‎Comprehensive and thorough numerical tests are provided to demonstrate the precision‎, ‎applicability‎, ‎and effectiveness of the proposed method‎, ‎along with the flexibility of this strategy‎. ‎The numerical outcomes from this approach are contrasted with the exact solution‎. ‎A comparison of the results from this scheme with the exact solution shows that the new approach is efficient‎, ‎yielding high-accuracy approximate solutions even with a limited number of basis functions‎, ‎and in cases where the problem's solution lacks infinite differentiability‎, ‎offering superior results and fewer basis functions compared to advanced methods‎. ‎Additionally‎, ‎numerous physical application issues involving multi-term variable-order fractional differential equations‎, ‎such as the damped mechanical oscillator problem and the Bagley-Torvik equation‎, ‎can be addressed using the proposed method‎.