Abstract
The purpose of this paper is study the fractional-order dynamics of the oxygen diffusion through capillary to tissues under the influence of external forces considering the fractional operators of Liouville–Caputo and Caputo–Fabrizio. We apply the Laplace homotopy method for analytical and numerical results. Three cases are considered: first, when axial and radial forces acting on capillary, the second one when only radial force acting on capillary and finally when axial force acting on capillary. In order to validate the importance and application of the presented method with the old and new Caputo fractional order derivatives, we given some examples. The solutions obtained confirm that the Laplace homotopy method is a powerful an efficient technique for analytic treatment of a wide variety of diffusion equations in mathematical physics.
•Fundamental solutions for the oxygen diffusion equation are obtained.•We consider several cases for the effect of radial forces.•New complex dynamics are obtained with the application of several fractional-order derivatives.