Abstract
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.
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