Theoretical analysis of the velocity field, stress field and vortex sheet of generalized second order fluid with fractional anomalous diffusion

Science in China, Series A: Mathematics, Physics, Astronomy

Volumn 44, Issue 11, 2001, Pages 1387-1399

  Xu, Mingyu ^a   Tan, Wenchang ^b  

^a SHANDONG UNIVERSITY   (China)

^b PEKING UNIVERSITY   (China)

Author keywords

Anomalous diffusion; Fractional calculus; Generalized Mittag Leffler function; Generalized second order fluid; Stress field; Vortex sheet

Indexed keywords

EID: 0035520475     PISSN: 10069283     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02877067     Document Type: Article

References (14)

1. Nonnemacher, T. F., Metzler, R., On the Riemann-Liouville fractional calculus and some recent applications, Fractals, 1995, 3(3): 557-566.
2. Mainardi, F., Fractional calculus: some basic problems in continuum and statistical mechanics, in Fractals and Fractional Calculus in Continuum Mechanics (eds. Cappinteri, A., Mainardi, F.), New York: Springer Wien, 1997, 291-348.
3. Rossikhin, Y. A., Shitikova, M. V., Applications of fractional calculus to dynamic problems of linear and nonlinear hereditary mechanics of solids, Appl. Mech. Rev., 1997, 50(1): 15-67.
4. Podlubny, I., Fractional Differential Equations, San Diego: Academic Press, 1999, 86-231.
5. Henry, B. I., Wearne, S. L., Fractional reaction-diffusion, Physica A, 2000, 276(3): 448-455.
6. Wyss, W., The fractional diffusion equation, J. Math. Phys., 1986, 27(11): 2782-2785.
7. Bagley, R. L., Torvik, P. J., On the appearance of the fractional derivative in the behavior of real materials, J. Appl. Mech., 1984, 51(2): 294-298.
8. Mathai, A. M., Saxena, R. K., The H-function with Applications in Statistics and Other Disciplines, New Delhi-Bangalore-Bombay: Wiley Eastern Limited, 1978, 1-12.
9. Gorenflo, R., Luchko, Y., Mainardi, F., Wright function as scale-invariant solutions of the diffusion-wave equation, J. Comput. Appl. Math., 2000, 118(1): 175-191.
10. Yih, C. S., Fluid Mechanics: A Concise Introduction to the Theory, New York: MeGraw-Hill, Inc., 1969, 321-324.
11. Wu Wangyi, Fluid Mechanics (in Chinese), Beijing: Peking Univ. Press, 1983, 226-230.
12. Mainardi, F., Gorenflo, R., On Mittag-Leffler-Type function in fractional evolution processes, J. Comput. Appl. Math. 2000, 118(2): 283-299.
13. Anhand, V. V., Leonenko, N. N., Scaling law for fractional diffusion-wave equations with singular data, Statistics and Probability Letters, 2000, 48(3): 239-252.
14. Kivyakova, V., Multiple (multiindex) Mittag-Leffler functions and relations to generalized fractional calculus, J. Comput. Appl. Math., 2000, 118(1): 241-259.