Dynamic optimization problems (DOPs) are known to be challenging due to the variability of their objective functions and constraints over time. The complexity of these problems increases further when the frequency of landscape change and the dimensionality of the search space are large. In this work, we propose a novel fractal decomposition-based method designed for DOPs, called FDS. It is a new single solution metaheuristic that introduces a new hypersphere-based space decomposition for efficient exploration, an archive for diversity control, and a pseudo-gradient-based local search (called GraILS) for fast exploitation. Extensive experiments on the well-known and the standard benchmark (the Moving Peak Benchmark: MPB) demonstrate that FDS consistently outperforms state-of-the-art competitors. Furthermore, FDS shows high robustness across diverse scenarios, maintaining superior performance despite variations in key benchmark parameters, such as the severity of landscape shifts, the number of peaks, the dimensionality of the problem, and the frequency of change. FDS achieves the highest average rank across all experiments and demonstrates dominant performance in 19 out of 23 scenarios. The implementation of FDS is available via the following GitHub repository: https://github.com/alc1218/FDS .