Fractional calculus and some intermediate physical processes

One of the main applications of the fractional calculus (integration and differentiation of arbitrary (fractional) order) is the modeling of the intermediate processes [J. Frac. Calculus 7 (1995) 89; Int. J. Theo. Phys. 35(2) (1996) 311; R. Gorenflo, R. Rutman, Fachbereich Mathematik Reprint No. A-28/94 (1994); F. Mainardi, Proc. 14th IMACS World Congr., vol. 1, 1994, p. 329; Chaos Soliton Fract. 7(6) (1996) 1; J. Math. Phys. 30 (1989) 134]. In this work we use the fractional calculus to formulate the models which represent the two intermediate physical process; convection-diffusion and transport-diffusion processes. The existence and uniqueness of their solution will be proved and the continuation to the convection, diffusion and transport processes are studied. (C) 2002 Elsevier Science Inc. All rights reserved.