<p>This paper presents an efficient new numerical approach for the solution of fractal-fractional differential equations (FFDEs) with exponential decay kernels, which occur commonly in nonlinear and memory-based physical systems. The technique couples the DaftardarGejji and Jafari iterative method (DJM), a high-level method that produces a rapid-convergent series solution without linearization or discretization, with a predictor-corrector approach to achieve increased accuracy and efficiency in computations. In addition, we adopt a modified version of DJM introduced by Bhalekar, which is formulated for fractional-order problems and possesses better convergence properties when applied to fractal-fractional operators in the sense of Riemann. Theoretical foundations such as fractal-fractional derivative definitions, stability analysis and convergence properties are established. The scheme is then exemplified on various complex systems such as financial dynamics, memristor model, chaotic attractors and cancer dynamics to attest to the reliability and strength of the scheme. Computational simulations confirm the method’s capability in replicating complex dynamics with a high accuracy rate and lower computational cost, giving the scheme a wide margin of generic application in science and engineering.</p>