Applications of integral transforms in fractional diffusion processes

Integral Transforms and Special Functions

Volumn 15, Issue 6, 2004, Pages 477-484

  Mainardi, Francesco ^a  

^a UNIVERSITY OF BOLOGNA   (Italy)

Author keywords

Fractional integrals and derivatives; Integral transforms; Mellin Barnes integrals

Indexed keywords

EID: 5744237978     PISSN: 10652469     EISSN: None     Source Type: Journal    
DOI: 10.1080/10652460412331270652     Document Type: Article

References (21)

1. Caputo, M. (1967). Linear models of dissipation whose Q is almost frequency independent, Part II. Geophys. J. R. Astr. Soc., 13, 529-539.
2. Caputo, M. and Mainardi, F. (1971). Linear models of dissipation in anelastic solids. Riv. Nuovo Cimento (Ser. II), 1, 161-198.
3. Erdélyi, A., Magnus, W., Oberhettinger, F. and Tricomi, F. G. (1953-1955). Higher Transcendental Functions. (Bateman Project) Vols. 1-3, McGraw-Hill, New York.
4. Feller, W. (1952). On a generalization of Marcel Riesz' potentials and the semi-groups generated by them. Meddelanden Lunds Universitets Matematiska Seminarium (Comm. Sém. Mathém. Université de Lund). Tome suppl. dédié a M. Riesz, pp. 73-81.
5. Feller, W. (1971). An Introduction to Probability Theory and its Applications, Vol. 2, Wiley, New York.
6. Gorenflo, R., Iskenderov, A. and Luchko, Yu. (2000). Mapping between solutions of fractional diffusion-wave equations. Fractional Calculus Appl. Anal., 3, 75-86.
7. Gorenflo, R., Luchko, Yu. and Mainardi, F. (1999). Analytical properties and applications of the Wright function. Fractional Calculus Appl. Anal., 2, 383-414.
8. Gorenflo, R., Luchko, Yu. and Mainardi, F. (2000). Wright functions as scale-invariant solutions of the diffusion-wave equation. J. Comput. Appl. Math., 118, 175-191.
9. Gorenflo, R. and Mainardi, F. (1997). Fractional calculus: integral and differential equations of fractional order. In: Carpinteri, A. and Mainardi, F. (Eds.), Fractals and Fractional Calculus in Continuum Mechanics, Springer Verlag, Wien, pp. 223-276. [Reprinted in http://www.fracalmo.org]
10. Mainardi, F. (1996). Fractional relaxation-oscillation and fractional diffusion-wave phenomena. Chaos, Solitons Fract., 7, 1461-1477.
11. Mainardi, F. (1997). Fractional calculus: some basic problems in continuum and statistical mechanics. In: Carpinteri, A. and Mainardi, F. (Eds.), Fractals and Fractional Calculus in Continuum Mechanics. Springer Verlag, Wien and New-York, pp. 291-248. [Reprinted in http://www.fracalmo.org]
12. Mainardi, F. and Gorenflo, R. (2000). On Mittag-Leffler-type functions in fractional evolution processes. J. Comput. Appl. Math., 118, 283-299.
13. Mainardi, F., Luchko, Yu. and Pagnini, G. (2001). The fundamental solution of the space-time fractional diffusion equation. Fractional Calculus Appl. Anal., 4, 153-192.
14. Mainardi, F. and Pagnini, G. (2003). Salvatore Pincherle: the pioneer of the Mellin-Barnes integrals. J. Comput. Appl. Math., 153, 331-342.
15. Mathai, A. M. and Saxena, R. K. (1978). The H-function with Applications in Statistics and Other Disciplines. Wiley Eastern Ltd, New Delhi.
16. Podlubny, I. (1999). Fractional Differential Equations. Academic Press, San Diego.
17. Riesz, M. (1949). L'intégrales de Riemann-Liouville et le problème de Cauchy. Acta Math., 81, 1-223.
18. Sato, K. (1999). Lévy Processes and Infinitely Divisible Distributions. Cambridge University Press, Cambridge.
19. Samko, S. G., Kilbas, A. A. and Marichev, O. I. (1993). Fractional Integrals and Derivatives: Theory and Applications. Gordon and Breach, New York.
20. Srivastava, H. M., Gupta, K. G. and Goyal, S. P. (1982). The H-Functions of One and Two Variables with Applications. South Asian Publishers, New Delhi and Madras.
21. Uchaikin, V. V. and Zolotarev, V. M. (1999). Chance and Stability. Stable Distributions and their Applications. VSP, Utrecht.