Mohammad Amirian Matlob - Student at Tabiat Modares University, Department of Mathematical Sciences,iran
Yousef Jamali - An Assistant Prof at Tabiat Modares University, Department of Mathematical Sciences,iran

Investigation of the cell behavior under deformation is crucial. For instance, we can refer to cancer cells that have different mechanical properties from healthy cells. Cancer is a disease in which many of the characteristics of normal cell behavior are lost or perturbed. Studies has indicated that in the cancer cells, microtubules and microfilaments properties will be changed. Microfilaments or actin filaments are the thinnest filaments of the cytoskeleton, a structure found in the cytoplasm of eukaryotic cells. These linear polymers of actin subunits are flexible and relatively strong, resisting buckling by multi-piconewton compressive forces and filament fracture by nanonewton tensile forces. Consequently the cells elasticity under deformation will have different behavior from the healthy cells. As a result of our research, in this paper we have represented a new fractional derivative constitutive model for cell viscoelasticity; that has more accuracy than the other suggested models. Finally, we claim proposed model can be suitable replacement for Bausch model in cell viscoelasticity prediction.

fractional calculus, cell viscoelasticity, modelling, cell biomechanics