Fractional Calculus And Its Applications In Biological Heat And Mass Transfer

This paper was composed of three independent but, correlative chapters. In chapter 1, the definition and history of fractional calculus were introduced.In chapter 2 and chaper 3, two applications of fractional calculus in biological heat and mass transfer were discussed.The first chapter is the basis for the other chapters of this thesis. In section§1.1, the definitions and main properties of the Riemann-liouville fractional operator and Caputo fractional operator were given. In section§1.2, the integral transforma-tion of the fractional calculus,including the Laplace transform and the. finite Hankel transform, were introduced. In section§1.3. the definition and some Formula of the generalized Mittag-Laffler function Eαβ(z) were given.The second chapter is an application of fractional calculous in radial heat trans-fer of biological tissue. In section§2.2, radial heat transfer equation in cylindrical coordinates was established By assuming the local thermal conditions, the temperature rise of the fractional differential equations was given By applying the Laplace transform and the finite Hankel transform methods, the exact solution of the model in the form of generalized Mittag-Leffler function was given In section§2.3,the number of fractional calculus given by special valueα=0 andα=1 were discussed. Whenα=0, the expression of temperature rise was whenα= 1, the expression of temperature rise was In the end, we discussed the influences of various parameters on the temperature rise based on graphics of the solution.The third chapter is an application of fractional calculous in the two-phrase biological mass transfer of sodium ions across intestines. In section§3.2, the basic equations were derived In section§3.3. the solutions of the image functions (?)1 and (?)2 were given by applying the Laplace transform method, In section§3.4,the steady-state concentration distributions of sodium ions in both intercellular and cellular phases were given and discussed by applying the final value theorem of the Laplace transform. C2∞(x)...