<p>Vanadium dioxide is a well-known candidate for memristor applications due to its insulator-to-metal transition characteristics, this is because vanadium dioxide memristors are versatile devices whose operating mechanism is based on an abrupt and volatile change of resistivity. This manuscript introduces the fractal–fractional framework for a third-order vanadium dioxide memristor neuron model that investigates the role of non-local dynamics on chaotic behavior. The third-order vanadium dioxide memristor neuron model is analyzed under three conditions of fractal-fractional differential operators (i) deviation of fractional parameter with fixed fractal order, (ii) deviation of fractal parameter with fixed fractional order, and (iii) simultaneous deviation of both parameters. The mathematical model of third-order vanadium dioxide memristor neuron has been discretized by means of Adams-Bashforth-Moulton method for the sake of numerical simulations. The results highlight the fractal–fractional framework as a versatile tool for tailoring vanadium dioxide memristor neuron’s dynamics namely irregular oscillations, dispersed attractors with enhanced chaoticity, bounded loops with tunable stability and excessive fluctuations. These findings confirm that fractional order acts as a memory controller, while fractal order governs structural scaling, together enabling precise modulation between chaos and stability.</p>