Turbulence is a non-local and nonlinear phenomenon. As a closure model to Reynolds-averaged Navier–Stokes equations, we formulate a fractional stress-strain relationship [2] using a a variable-order (spatially-dependent) Caputo fractional derivative, which is a non-local operator. For wall bounded flows, near the wall (within the viscous sub-layer) the flow is purely local, while the outer region is governed by a non-local process. Indeed, our model addresses the amalgamation of local and non-local effects [1, 2]. For the two-sided model constructed in [2] we find scaling relationship for the fractional order akin to velocity scaling for the considered cases. Notably, a power-law behaviour of fractional order akin to logarithmic regime for velocity. By virtue of this power-law the fractional order asymptotes at infinite Reynolds number limit thereby justifying its validity. Further, a law of wake has been observed for the fractional order. Indeed, the two-sided model constructed in [2] demonstrates its physical consistency. The success of two-sided model motivated to invoke tempered fractional calculus in [2]. Tempering ensures finite jump lengths, an important remark for unbounded flows. Since turbulence is a decay process, it led to define a ”horizon of non-local interactions” in [2]. We pedagogically studied with two tempering distributions resulting a smooth and sharp cutoff, by an exponential and Heaviside function respectively for wall bounded flows. Its equivalence is studied computationally. For numerical investigation, we designed algorithms in [2], notably, the pointwise fractional physics-informed neural network to find the fractional order as an inverse problem. REFERENCES [1] P. P. Mehta, G. Pang, F. Song and G. E. Karniadakis, Discovering a universal variable order fractional model for turbulent Couette flow using a physics-informed neural network. Fractional calculus and applied analysis, Vol. 22(6), pp. 1675-1688, 2019. [2] P. P. Mehta, Fractional and tempered fractional models for Reynolds-averaged Navier–Stokes equations. Journal of Turbulence, DOI: 10.1080/14685248.2023.2274100, 2023.