Differential evolution (DE) is among the best evolutionary algorithms for global optimization. However, the basic DE has several shortcomings like the slow convergence speed and it is more likely to be stuck at a local optimum. Moreover, the performance of DE is sensitive to its mutation strategies and mutation and crossover control parameters. In this scope, we present in this paper three mechanisms to overcome DE limitations. Firstly, two novel mutations called DE/mean-current/1 and DE/best-mean-current/1 are proposed and integrated in DE algorithm, they have both exploration ability and exploitation trend. On the other hand, to avoid to be trapped in local minima of hard functions, a new exploration operator has proposed called Weibull flight based on the Weibull distribution. Finally, new adapted control parameters based also on the Weibull distribution are integrated. The efficacy of the proposed algorithms called meanDE, MDEW, AMDE and AMDEW is validated throughout intensive experimentations using classical tests, some challenging tests, the CEC2017, CEC2020, the most recent CEC2022, four constraint engineering problems, and data clustering problem. Moreover, comparison with several popular, recent, and high-performance optimization algorithms showed a high effectiveness of the proposed algorithms in locating the optimal or near-optimal solutions with higher efficiency. The efficiency of the new mutations is clear compared to the standard DE mutations. Moreover, the proposed Weibull flight has great capacity to deal with hard composition functions of CEC benchmarks. Finally, the use of the adapted control parameter of mutation scale helps to avoid the parameters setting problem present in several metaheuristics.