## 1 Introduction
The abovementioned studies highlighting a transient decrease in water ADC during activation were conducted using bipolar diffusion gradients and suitable strategies toeliminate the contribution of the \(\mathrm{G_{i}}\), such as using a high g strength [23; 30] and diffusion-sensitized double spin-echo EPI sequence [26]. Indeed, as underlined by [PERSON] [31], the ADC increase due to \(\Delta\chi\) changes is in contrast to the minute effect suggested by [PERSON]. Therefore, the \(\mathrm{G_{i}}\) contributions in DW-fMRI measurements may mask or even cancel out the effect of an ADC decrease [32; 33]. In particular, [PERSON] showed that the interaction between diffusion gradients and \(\Delta\chi\)-induced \(\mathrm{G_{i}}\) around vessels has an impact on ADC measurements and fMRI experiments [31]. However, using both low-medium and high b-values, activation maps are compatible with conventional BOLD fMRI-derived maps, and the activated brain areas obtained using DW-fMRI were reported to be more \"localized\" and detailed compared to BOLD areas [18; 23; 26; 34; 35]. In contrast to conventional DWI approaches based on Normal Gaussian diffusion [36], non-Gaussian models provide a superior intrinsic specificity and sensitivity to detect microscopic tissue changes [37; 38; 39; 40; 41]. Indeed, a recent study showed the time dependence of the diffusional kurtosis in neural activity in rodents [42], using higher b-values (\(b\ \leq 2000\ \mathrm{s/mm^{2}}\)) than those used in previous studies and showing a greater sensitivity of the kurtosis parameter to the neural activation. In this brief communication, we aim to take a step forward, adopting fractional diffusion representation [43; 44; 45; 46] with higher b-values (\(b\ \leq 3000\ \mathrm{s/mm^{2}}\)) to provide preliminary novel insights into the ongoing DW-fMRI debate. Fractional diffusion describes diffusion with a fractional order derivative, which allows for more flexibility in capturing non-Gaussian diffusion. Fractional derivatives differ from conventional derivatives in that they allow for differentiation in a non-integer (fractional) order. Unlike conventional derivatives, which measure the rate of change at a specific point, fractional derivatives describe processes with memory and spatial correlations, making them suitable for modeling complex diffusion in biological tissues. In neuro-MRI, these fractional orders serve as quantifiable parameters, meaning that they can be measured and interpreted to provide insights into the brain's microstructure. The fractional diffusion representation is based on the generalization of the diffusion equation to fractional order derivatives (e.g., as in the Continuous-time random walk--CTRW--framework [47; 48]) and introduces the time fractional exponent \(\alpha\) and the spatial fractional exponent \(\gamma\). These new parameters are specific imaging biomarkers of tissue complexity and magnetic property heterogeneities [43; 44; 45; 46; 49; 50; 51; 52; 53; 54]. Here, we hypothesize that the \(\gamma\) parameter, the fractional exponent of the space derivative, could be of particular interest for DW-fMRI applications due to its proven dependence on both the local \(\Delta\chi\)[43; 44; 46] and diffusion multi-compartmentalization [52]. Hence, we studied whether \(\gamma\) can quantify cellular morphology changes and neurovascular regulation during neuronal activation with higher sensitivity and specificity than conventional BOLD fMRI and DW-fMRI, with an exemplar application to task-based activation of the human visual cortex. The dependence of the ADC parameter on microstructures and other physiological variables is well recognized; however, this is not the case for the \(\gamma\) parameter. For this reason, to better interpret the data related to \(\gamma\) experiments, we performed simulations to highlight the dependence modality of \(\gamma\) on \(\Delta\chi\) variations and changes in the extracellular space due to cellular swelling.