Baleanu, DumitruIbrahim, Rabha W.Salahshour, Soheil2026-04-212026-04-2120262577-819610.1002/eng2.707262-s2.0-105034506181https://hdl.handle.net/123456789/9039https://doi.org/10.1002/eng2.70726Cell blebbing is a fundamental morphodynamic process governed by the interplay of cytoplasmic pressure, cortical contractility, and membrane tension. Classical geometric flow models capture instantaneous mechanical effects but fail to represent hereditary and viscoelastic memory inherent to living cells. In this work, we propose a ( q, tau )-fractional geometric flow framework for bleb morphogenesis, where the parameters q and tau quantify deformation memory and stress-relaxation tempering, respectively. Fluorescence microscopy frames from the WRAP dataset and synthetic simulations are segmented to extract time series of bleb height, effective radius, and fractional mean curvature. These observables are fitted using a predictor-corrector numerical scheme for a ( q, tau ) -fractional evolution equation subject to an energy dissipation law. The numerical solver and segmentation pipeline are validated on synthetic and experimental data. The proposed model accurately reproduces both the rapid expansion and slow relaxation phases of bleb evolution, with residual errors below 10(-3) and fitted parameters in biologically plausible ranges. Moreover, the total fractional energy exhibits monotonic decay, consistent with thermodynamic dissipation. The results demonstrate that ( q, tau )-fractional geometric flows provide a unified and physically interpretable framework for coupling image-based quantification with nonlocal curvature-driven dynamics in cellular morphogenesis.eninfo:eu-repo/semantics/openAccessImage-Based SegmentationEnergy DissipationCurvature-Driven EvolutionCell Bleb MorphogenesisBiophysical Modelingτ)-Fractional Flow(qGeometric Partial Differential EquationsViscoelastic MemoryTau)-Fractional FlowArticle