Solving a fourth-order fractional diffusion-wave equation in a bounded domain by decomposition method

Numerical Methods for Partial Differential Equations

Volumn 24, Issue 4, 2008, Pages 1115-1126

  Jafari, Hossein ^a   Dehghan, Mehdi ^b   Sayevand, Khosro ^c  

^a UNIVERSITY OF MAZANDARAN   (Iran)

^b AMIRKABIR UNIVERSITY OF TECHNOLOGY   (Iran)

^c MALAYER UNIVERSITY   (Iran)

Author keywords

Adomian decomposition method; Bounded domain; Caputo fractional derivative; Fractional diffusion wave equation; Mittag Leffler function

Indexed keywords

EID: 47049131727     PISSN: 0749159X     EISSN: 10982426     Source Type: Journal    
DOI: 10.1002/num.20308     Document Type: Article

References (26)

1. 1 O. P. Agrawal, Solution for a fractional diffusion‐wave equation defined in a bounded domain, Nonlin Dynam 29 ( 2002), 145–155.
2. 2 F. Mainardi, Fractional diffusive waves in viscoelastic solids, Nonlinear waves in solids, J. I. Wegner and F. R. Norwood, editors, ASME book No AMR, Vol. 137, Fairfield, NJ, 1995, pp. 93–97.
3. 3 F. Mainardi, On the initial value problem for the fractional diffusion‐wave equation, Waves and stability in continuous media, S. Rionero and T. Ruggeeri, editors, World Scientific, Singapore, 1994, pp. 246–251.
4. 4 F. Mainardi, Fundamental solutions for the fractional diffusion‐wave equation, Appl Math Lett 9 ( 1996), 23–28.
5. 5 W. R. Schneider and W. Wyss, Fractional diffusion and wave equations, J Math Phys 30 ( 1998), 134–144.
6. 6 A. M. A. El‐Sayed, Fractional‐order diffusion‐wave equation, Int J Theo Phys 35 ( 1996), 311–322.
7. 7 R. R. Nigmatullin, The realization of the generalized transfer equation in a medium with fractal geometry, Phys Status Solidi B 133 ( 1986), 425.
8. 8 M. Ginoa, S. Cerbelli, and H. E. Roman, Fractional diffusion equation and relaxation in complex viscoelastic materials, Physica A 191 ( 1992), 449–453.
9. 9 K. B. Oldham and J. Spainer, The fractional calculus, Academic Press, New York, 1974.
10. 10 I. N. Sneddon, Fourier transforms, McGraw Hill, New York, 1951.
11. 11 G. Adomian, Solving frontier problems of physics: the decomposition method, Kluwer, Boston ( 1994).
12. 12 N. T. Shawaghfeh, Analytical approximate solutions for nonlinear fractional differential equations, Appl Math Comput 131 ( 2002), 517–529.
13. 13 E. Babolian, J. Biazar, and A. R. Vahidi, The decomposition method applied to systems of Fredholm integral equations of the second kind, Appl Math Comput 148 ( 2004), 443–452.
14. 14 J. Biazar, E. Babolian, and R. Islam, Solution of Volterra integral integral equations of the first kind by adomian method, Appl Math Comput 139 ( 2003), 249–258.
15. 15 V. Daftardar‐Gejji and H. Jafari, Adomian Decomposition: A tool for solving a system of fractional differential equations, J Math Anal Appl 301 ( 2005), 508–518.
16. 16 H. Jafari and V. Daftardar‐Gejji, Solving a system of non linear fractional differential equations using adomian decomposition, J Comput Appl Math 196 ( 2006), 644–651.
17. 17 J. Biazar and R. Islam, Solution of wave equation by Adomian decomposition method and the restrictions of the method, Appl Math Comput 149 ( 2004), 807–814.
18. 18 M. Dehghan, Application of the adomian decomposition method for two‐dimensional parabolic equation subject to nonstandard boundary specifications, Appl Math Comput 157 ( 2004), 549–560.
19. 19 O. P. Agrawal, A general solution for a fourth order fractional diffusion‐wave equation defined in a bounded domain, Comput Struct 79 ( 2001), 1497–1501.
20. 20 Yu. Luchko and R. Gorenflo, An operational method for solving fractional differential equations with the Caputo derivatives, Acta Math Vietnamica 24 ( 1999), 207–233.
21. 21 I. Podlubny, Fractional differential equations, Academic Press, San Diego, 1999.
22. 22 G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional integrals and derivatives: theory and applications, Gordon and Breach, Yverdon, 1993.
23. 23 F. Mainardi and G. Pagnin, The Wright functions as solutions of the time‐fractional diffusion equation, Appl Math Comput 141 ( 2003), 51–62.
24. 24 F. Mainardi and R. Gorenflo, On Mittag‐Leffler‐type functions in fractional evolution processes, J Comput Appl Math 118 ( 2000), 283–299.
25. 25 O. L. Moustafa, On the Cauchy problem for some fractional order partial differential equations, Chaos Soltions Fractals 18 ( 2003), 135–140.
26. 26 K. Abboui and Y. Cherruault, New ideas for proving convergence of decomposition methods, Comput Appl Math 29 ( 1995), 103–105.