We utilize Lyapunov exponents to quantitatively assess the hyperchaos and categorize the limit sets of complex dynamical systems. While there are numerous methods for computing Lyapunov exponents in integer-order systems, these methods are not suitable for fractional-order systems because of the nonlocal characteristics of fractional-order derivatives. This paper introduces innovative eight-dimensional chaotic systems that investigate fractional-order dynamics. These systems exploit the memory effect inherent in the Grünwald–Letnikov (G-L) derivative. This approach enhances the system’s applicability and compatibility with traditional integer-order systems. An 8D Chen’s fractional-order system is utilized to showcase the effectiveness of the presented methodology for hyperchaotic systems. The simulation results demonstrate that the proposed algorithm outperforms existing algorithms in both accuracy and precision. Moreover, the study utilizes the 0–1 Test for Chaos, Kolmogorov–Sinai (KS) entropy, the Kaplan–Yorke dimension, and the Perron Effect to analyze the proposed eight-dimensional fractional-order system. These additional metrics offer a thorough insight into the system’s chaotic behavior and stability characteristics.

In this paper, the weighted multilinear p-adic Hardy operators are introduced, and their sharp bounds are obtained on the product of p-adic Lebesgue spaces, and the product of p-adic central Morrey spaces, the product of p-adic Morrey spaces, respectively. Moreover, we establish the boundedness of commutators of the weighted multilinear p-adic Hardy operators on the product of p-adic central Morrey spaces. However, it’s worth mentioning that these results are different from that on Euclidean spaces due to the special structure of the p-adic fields.

In this paper, we introduce the p-adic Hardy type operator and obtain its sharp bound on the p-adic Lebesgue product spaces. Meanwhile, an analogous result is computed for the p-adic Lebesgue product spaces with power weights. In addition, we characterize a sufficient and necessary condition which ensures that the weighted p-adic Hardy type operator is bounded on the p-adic Lebesgue product spaces. Furthermore, the p-adic weighted Hardy-Cesàro operator is also obtained.