A novel boundary-layer approximation technique to detect fractionality in distinct nanofluid flows over inclined surfaces

This study advances the analysis of unsteady one-dimensional MHD boundary-layer flow of nanofluids over an impulsively started, moving infinite plate embedded in a porous medium, with possible memory effects induced by nanoparticle interactions. To capture these non-local relaxation phenomena, three fractional-derivative models, based on the Caputo, Caputo–Fabrizio, and Atangana–Baleanu operators, are formulated alongside the classical governing model. Analytical expressions for the velocity, temperature, and concentration fields are derived using combined Fourier–Laplace transforms and represented in terms of Mittag–Leffler functions. However, because full spatial profiling within thin boundary layers is experimentally challenging, the fractional order in such models often remains a fitted parameter without direct physical validation. To address this limitation, the work introduces a novel boundary-layer–curve–based diagnostic framework applicable to any boundary-layer flow, which refocuses analysis from full-field solutions to the temporal evolution of hydrodynamic, thermal, and solutal boundary-layer thicknesses, scalar quantities that can be measured far more reliably in practical settings. The method is evaluated across ten nanofluid formulations encompassing diverse base fluids, nanoparticle materials, and particle geometries, including a controlled Al 2 O 3 –water pair used to isolate shape-driven transport effects. Using this comprehensive dataset, a new fractionality detection technique is proposed demonstrating how fractional boundary-layer curves can serve as sensitive indicators of possible memory-driven non local effects in nanofluid flows. The analysis further shows that, all fractional models exhibit two characteristic times at which they intersect their classical counterparts, providing additional markers for diagnosing fractionality. The study offers a practical bridge between fractional derivative based boundary layer theory and experimental realizability, while outlining future needs including direct validation, incorporation of alternative fractional operators, and extension to more complex flow geometries.