Sorting algorithms play a crucial role in efficient data organization for calculations. Frequency-Based Merge Sort: This is a new algorithm that ranks element occurrence over value when sorting elements. FBMS is an extension of merge sort in which frequency analysis has been included so that the possibility of calculating occurrence pattern-based sorting takes place in, although maintaining the complexity of O(nlogn) for best, average, and worst cases. Specifically, the algorithm is very efficient for applications in frequency analysis such as inventory management, customer information, and text processing. Comparative studies show that FBMS presents an efficient high performance with resource optimization in frequency-prioritized situations compared to conventional sorting techniques. Further, it examines potential capabilities in supporting digital transformation, maximizing energy efficiency, and stimulating sustainable computing of relevance to contemporary business and environmental challenges.