This paper presents a novel dynamic Jellyfish Search Algorithm using a Simulated Annealing and disruption operator, called DJSD. The developed DJSD method incorporates the Simulated Annealing operators into the conventional Jellyfish Search Algorithm in the exploration stage, in a competitive manner, to enhance its ability to discover more feasible regions. This combination is performed dynamically using a fluctuating parameter that represents the characteristics of a hammer. The disruption operator is employed in the exploitation stage to boost the diversity of the candidate solutions throughout the optimization operation and avert the local optima problem. A comprehensive set of experiments is conducted using thirty classical benchmark functions to validate the effectiveness of the proposed DJSD method. The results are compared with advanced well-known metaheuristic approaches. The findings illustrated that the developed DJSD method achieved promising results, discovered new search regions, and found new best solutions. In addition, to further validate the performance of DJSD in solving real-world applications, experiments were conducted to tackle the task scheduling problem in cloud computing applications. The real-world application results demonstrated that DJSD is highly competent in dealing with challenging real applications. Moreover, it achieved gained high performances compared to other competitors according to several standard evaluation measures, including fitness function, makespan, and energy consumption.