Applications that need constant performance and exact timing require real-time operating systems (RTOS). Maintaining RTOS's predictability, efficiency, and dependability relies heavily on memory management. Memory fragmentation, few memory resources, severe real-time limitations, and concurrency problems are some of the main obstacles to RTOS memory management that this research seeks to address. Problems like increasing latency, unexpected behaviour, and inefficient use of resources are major roadblocks on the path to peak system performance. Dynamic memory allocation, memory partitioning, and garbage collection are some of the current memory management approaches that are examined in the research. Their merits and shortcomings are highlighted. We investigate novel approaches and optimisation techniques to tackle these difficulties. In order to improve the efficiency and predictability of memory management, we offer adaptive algorithms, memory pooling, and hardware-assisted management strategies. We assess and contrast the efficacy of various approaches by conducting empirical evaluations in simulated and real-world case studies. The results show that adaptive and hardware-assisted methods are able to guarantee constant real-time performance, enhance resource utilisation, and drastically decrease memory fragmentation. The research finishes with some useful suggestions for developers and designers of systems, stressing the importance of a balanced strategy that incorporates various memory management methodologies. This study helps improve real-time operating systems (RTOS) by removing obstacles and maximising efficiency, making them better prepared to handle the demanding requirements of mission-critical real-time applications.