Global Mittag–Leffler synchronization of fractional-order Clifford-valued neural networks with mixed time-varying delays via adaptive quantized pinning control

The objective of this paper is to establish verifiable synchronization criteria for fractional-order Clifford-valued neural networks with mixed time-varying delays when the response system is controlled through finite-resolution communication channels. The model contains discrete and distributed delays, non-commutative Clifford-valued connection weights, and Caputo fractional dynamics. Instead of decomposing the Clifford-valued system into 2ᵐ 2 m real-valued subnetworks, the analysis is carried out directly in the multivector space by using operator-norm bounds for Clifford left multiplication, a fractional Halanay-type comparison inequality, and a sector representation of the logarithmic quantizer. An adaptive quantized pinning controller is designed, and a quantization-weighted adaptive Lyapunov functional is introduced to show that the adaptive term contributes a positive effective attenuation margin. The main theorem gives an explicit LMI-free algebraic condition for global Mittag–Leffler synchronization. A robustness theorem further provides a practical residual bound under bounded disturbances. The revised numerical section includes step-refinement evidence for the predictor–corrector Adams–Bashforth–Moulton implementation, comparisons with non-quantized and non-adaptive controllers, sensitivity tests for the initial adaptive gains, a discussion of the conservatism caused by Clifford operator-norm estimates, and an additional larger-scale simulation. These results clarify the range, advantages, and limitations of the proposed direct Clifford-valued approach.