Fractional calculus and some intermediate physical processes

Authors:
Ahmed M. A. El-Sayed;Fatma M. Gaafar
Affiliations:
Mathematics Department, Faculty of Science, Alexandria University, Alexandria, Egypt;Mathematics Department, Faculty of Science, Alexandria University, Alexandria, Egypt
Venue:
Applied Mathematics and Computation
Year:
2003

Citing 2
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Adomian's decomposition method for solving an intermediate fractional advection-dispersion equation

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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.