Exact solution for the fractional cable equation with nonlocal boundary conditions

Central European Journal of Physics

Volumn 11, Issue 10, 2013, Pages 1304-1313

  Bazhlekova, Emilia G ^a   Dimovski, Ivan H ^a  

^a INSTITUTE OF MATHEMATICS AND INFORMATICS   (Bulgaria)

Author keywords

anomalous diffusion; cable equation; fractional derivative; three parameter Mittag Leffler function

Indexed keywords

EID: 84890873973     PISSN: 18951082     EISSN: 16443608     Source Type: Journal    
DOI: 10.2478/s11534-013-0213-5     Document Type: Article

References (23)

1. R. Metzler, J. Klafter, Phys. Rep. 339, 1 (2000).
2. A. V. Chechkin, R. Gorenflo, I. M. Sokolov, J. Phys. A 38, 679 (2005).
3. B. I. Henry, T. A. M. Langlands, S. L. Wearne, Phys. Rev. E 74, 031116 (2006).
4. B. I. Henry, T. A. M. Langlands, S. L. Wearne, Phys. Rev. Lett. 100, 128103 (2008).
5. T. A. M. Langlands, B. I. Henry, S. L. Wearne, J. Math. Biol. 59, 761 (2009).
6. T. A. M. Langlands, B. I. Henry, S. L. Wearne, SIAM J. Appl. Math. 71, 1168 (2011).
7. F. Liu, Q. Yang, I. Turner, J. Comput. Nonlinear Dyn. 6, 0110091 (2011).
8. X. Hu, L. Zhang, Appl. Math. Model. 36, 4027 (2012).
9. Y. M. Lin, X. J. Li, C. J. Xu, Math. Comput. 80, 1369 (2011).
10. E. Bajlekova, Ph. D. thesis, Eindhoven University of Technology (Eindhoven, The Netherlands, 2001) 10 http://alexandria. tue. nl/extra2/200113270. pdf.
11. A. Schot et al., Phys. Lett. A 366, 346 (2007).
12. V. Daftardar-Gejji, S. Bhalekar, J. Math. Anal. Appl. 345, 754 (2008).
13. Yu. Luchko, J. Math. Anal. Appl. 374, 538 (2011).
14. H. Jiang, F. Liu, I. Turner, K. Burrage, Comput. Math. Appl. 64, 3377 (2012).
15. M. Dehghan, Chaos Soliton. Fract. 32, 661 (2007).
16. A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and applications of fractional differential equations (Elsevier, Amsterdam, 2006).
17. I. Podlubny, Fractional Differential Equations (Academic Press, New York, 1999).
18. R. K. Saxena, A. M. Mathai, H. J. Haubold, Astrophys. Space Sci. 209, 299 (2004).
19. N. S. Bozhinov, Differ. Equ. 26, 741 (1990) (in Russian).
20. I. H. Dimovski, Convolutional Calculus (Kluwer, Dordrecht, 1990).
21. I. H. Dimovski, R. I. Petrova, In: Generalized functions and convergence, Katowice 1988 (World Sci. Publ., Teaneck, NJ, 1990) 89.
22. Y. Tsankov, C. R. Acad. Bulg. Sci. (2013) (to appear).
23. K. Diethelm, The analysis of fractional differential equations (Springer-Verlag Berlin Heidelberg, 2010).