Analytic solution of fractional-order heat- and wave-like equations using generalized n-dimensional differential transform method

Zeitschrift fur Naturforschung - Section A Journal of Physical Sciences

Volumn 66, Issue 10-11, 2011, Pages 581-590

  Baranwal, Vipul K ^a   Pandey, Ram K ^a   Tripathi, Manoj P ^a   Singh, Om P ^a  

^a BANARAS HINDU UNIVERSITY   (India)

Author keywords

Caputo fractional derivative; Generalized n dimensional differential transform method; N dimensional fractional heat and wave like equation

Indexed keywords

EID: 82155162554     PISSN: 09320784     EISSN: None     Source Type: Journal    
DOI: 10.5560/ZNA.2011-0020     Document Type: Article

References (35)

1. R. Gorenflo, F. Mainardi, E. Scalas, and M. Roberto, Fractional calculus and continuous time finance, III, The diffusion limit, in: Math, Finance, Konstanz, 2000, in: Trends Math, Birkhauser, Basel, 2001, pp. 171-180.
2. M. Roberto, E. Scalas, and F. Mainardi, Physica A 314, 749 (2002).
3. L. Sabatelli, S. Keating, J. Dudley, and P. Richmond, Eur. Phys. J. B 27, 273 (2002).
4. M. Meerschaaert, D. Benson, H. P. Scheffler, and B. Baeumer, Phys. Rev. E 65, 1103 (2002).
5. B. West, M. Bologna, and P. Grigolini, Physics of Fractal Operators, Springer, New York 2003.
6. G. Zaslavsky, Hamiltonian Choas and Fractional Dynamics, Oxford University press, Oxford 2005.
7. R. Hilfer, Application of Fractional Calculus in Physics, World Scientific, Singapore 2000.
8. J. T. Mechado, Frac. Cal. Appl. Anal. 4, 47 (2001).
9. Y. Lin andW. Jiang, Comput. Phys. Commun. 181, 557 (2010).
10. A. Yildirim and H. Kocak, Adv. Water Resour. 32, 1711 (2009).
11. B. Baeumer, M. M. Meerschaert, D. A. Benson, and S. W. Wheatcraft, Water Resource Res. 37, 1543 (2001).
12. R. Schumer, D. A. Benson, M. M. Meerschaert, B. Baeumer, and S. W. Wheatcraft, J. Contaminant Hydrol. 48, 69 (2001).
13. R. Schumer, D. A. Benson, M. M. Meerschaert, and B. Baeumer, Water Resource Res. 39, 1022 (2003).
14. S. Momani, Appl. Math. Comput. 165, 459 (2005).
15. O. P. Agrawal, Nonlin. Dyn. 29, 145 (2002).
16. H. Andrezei, Proc. R. Soc. Lond., Ser. A. Math. Phys. Eng. Sci. 458, 429 (2002).
17. J. Klafter, A. Blumen, and M. F. Shlesinger, J. Stat. Phys. 36, 561 (1984).
18. R. Metzler and J. Klafter, Physica A 278, 107 (2000).
19. R. Molliq, M. S. M. Noorani, and I. Hashim, Nonlin. Anal.: Real World Appl. 10, 1854 (2009).
20. H. Xu, S. J. Liao, and X. C. You, Commun. Nonlin. Sci. Numer. Simul. 14, 1152 (2009).
21. J. K. Zhou, Differential Transformation and Its Applications for Electric Circuits, Huazhong Univ. Press, Wuhan, China 1986.
22. F. Ayaz, Appl. Math. Comput. 147, 547 (2004).
23. A. Arikoglu, I. Ozkol, Appl. Math. Comput. 168, 1145 (2005).
24. N. Bildik, A. Konuralp, F. O. Bek, and S. Kucukarslan, Appl. Math. Comput. 172, 551 (2006).
25. I. H. Hassan, Chaos Soliton Fract. 36, 53 (2008).
26. H. Liu and Y. Song, Appl. Math. Comput. 184, 748 (2007).
27. A. Kurnaz, G. Oturanc, and M. E. Kiris, Int. J. Comp. Math. 82, 369 (2005).
28. A. Arikoglu and I. Ozkol, Chaos Soliton Fract. 34, 1473 (2007).
29. Z. Odibat, S. Momani, and V. S. Erturk, Appl. Math. Comput. 197, 467 (2008).
30. Z. Odibat and S. Momani, Appl. Math. Lett. 21, 194 (2008).
31. S. Momani, Z. Odibat, and V. S. Erturk, Phys. Lett. A 370, 379 (2007).
32. N. Heymans and I. Podlubny, Rheol. Acta 45, 765 (2006).
33. I. Podlubny, Fractional Differential Equations, Academic Press, New York, USA 1999.
34. P. L. Butzer and U. Westphal, An Introduction to Fractional Calculus, World Scientific, Singapore 2000.
35. K. S. Miller and B. Ross, An Introduction to the Fractional, Calculus and Fractional Differential Equation, Wiley, New York 1993.