A general solution of a space-time fractional anomalous diffusion problem using the series of bilateral eigen-functions

키워드

참고문헌 (18)

1. O. P. Agrawal, "Response of a diffusion-wave system subjected to deterministic and stochastic fields", Z. Angew. Math. Mech, 83(4), pp.265~274 (2001)
2. O. P. Agrawal, "Solution for a fractional diffusion-wave equation defined in a bounded domain", Nonlinear Dynam, 29, pp.145~155 (2002)
3. M. Ciesielski, "Numerical solutions to boundary value problem for anomalous diffusion equation with Riesz-Feller fractional operator", Journal of Theoretical and Applied Mechanics, 44(2), pp.393~403 (2006)
4. W. Feller, "On a generalization of Marcel Riesz' potentials and the semi groups generated by them", Meddeladen Lund Universitets Matematiska Seminarium, Tome Suppl. Dedie A M. Riesz, Lund, (1952), pp.73~81 (1952)
5. R. Gorenflo, "Random walk models for space-fractional diffusion processes", Fract. Calc. Appl. Anal, 1, pp.167~191 (1998)
6. R. Gorenflo, "Approximation of Levy-Feller diffusion by random walk", Z. Anal. Anwendungen, 18, pp.231~146 (1999)
7. H. J. Haubold, "Solution of fractional reaction-diffusion equations in terms of the H-function", Proceedings of the Second UN, NASA Workshop on the International Heliophysical Year 2007 and basic Space Science, pp.2007, 35[DOI]
8. A. A. Kilbas, "Theory and Applications of Fractional Differential Equation", Elsevier B. V. (2006)
9. F. Mainardi, "The fundamental solution of the space-time fractional diffusion equation", Fract. Calc. Appl. Anal, 4, pp.153~192 (2001)
10. A. M. Mathai, "The H-Function, Theory and applications" (2010), Springer
11. R. Metzler, "The random walk's guide to anomalous diffusion: A fractional dynamic approach", Phys. Rep, 339, pp.1~77 (2000)
12. K. S. Miller, "An Introduction to the Fractional Calculus and Fractional Differential Equations" (1993), John Wiley & Sons, Inc.
13. N. Ozdemir, "The numerical solutions of a two-dimensional space-time Riesz-Caputo fractional diffusion equation", An International Journal of Optimization and Control: Theories & Applications(IJOCTA), 1(1), pp.17~26 (2011)
14. I. Podlubny, "Fractional Differential Equations" (1999), Academic Press
15. S. G. Samko, "Fractional Integral and Derivatives" (1993), Gordon and Breach
16. H. M. Srivastava, "A Treatise on Generating Functions", Ellis Horwood Limited, pp.1984~ (1984)
17. H. M. Srivastava, "Some bilateral generating functions for a class of Generalized hypergeometric polynomials", J. Reine Angew. Math, 283, pp.265~274 (1976)
18. A. J. Turski, "Application of fractional derivative operators to anomalous diffusion and propagation problems", arXiv:math-ph, 2007

관련 논문AI추천