Solving fractional boundary value problems with Dirichlet boundary conditions using a new iterative method

Computers and Mathematics with Applications

Volumn 59, Issue 5, 2010, Pages 1801-1809

  Daftardar Gejji, Varsha ^a   Bhalekar, Sachin ^a  

^a UNIVERSITY OF PUNE   (India)

Author keywords

Anomalous diffusion; Boundary value problems; Caputo derivative; Diffusion wave equation; Dirichlet boundary conditions

Indexed keywords

ANOMALOUS DIFFUSION; CAPUTO DERIVATIVES; DIFFUSION WAVE EQUATION; DIRICHLET BOUNDARY CONDITION; FINITE DOMAINS; FRACTIONAL DIFFUSION; NONLINEAR FUNCTIONAL EQUATIONS;

BOUNDARY CONDITIONS; BOUNDARY VALUE PROBLEMS; DIFFUSION; ITERATIVE METHODS; NONLINEAR EQUATIONS;

WAVE EQUATIONS;

EID: 76449083483     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2009.08.018     Document Type: Article

References (19)

1. Schneider W.R., and Wyss W. Fractional diffusion and wave equations. J. Math. Phys. 30 1 (1989) 134-144
2. Mainardi F. Fractional relaxation-oscillation and fractional diffusion-wave phenomena. Chaos Solitons Fractals 7 (1996) 1461-1477
3. Fujita Y. Cauchy problems of fractional order and stable processes. Japan J. Indust. Appl. Math. 7 (1990) 459-476
4. Mainardi F., and Paradisi P. Fractional diffusive waves. J. Comput. Acoust. 9 4 (2001) 1417-1436
5. Nigmatullin R. Realization of the generalized transfer equation in a medium with fractional geometry. Physica Status (B) Basic Res. 133 1 (1986) 425-430
6. Giona M., Cerbelli S., and Roman H.E. Fractional diffusion equation and relaxation in complex viscoelastic materials. Physica A 191 (1992) 449-453
7. F. Mainardi, Fractional diffusive waves in viscoelastic solids, in: J.I. Wegner, F.R. Norwood. (Eds.) IUTAM Symposium-Nonlinear Waves in Solids, Fairfield, 1995, pp. 93-97
8. Metzler R., and Klafter J. Boundary value problems for fractional diffusion equations. Physica A 278 (2000) 107-125
9. Adomian G. Solving Frontier Problems of Physics: The Decomposition Method (1994), Kluwer
10. Agrawal O.P. Solution for fractional diffusion-wave equation defined in a bounded domain. Nonlinear Dynam. 29 (2002) 145-155
11. Daftardar-Gejji V., and Jafari H. Boundary value problems for fractional diffusion-wave equation. Aust. J. Math. Anal. Appl. 3 (2006) 1-8
12. Daftardar-Gejji V., and Bhalekar S. Boundary value problems for multi-term fractional differential equations. J. Math. Anal. Appl. 345 (2008) 754-765
13. Daftardar-Gejji V., and Bhalekar S. Solving fractional diffusion-wave equations using the new iterative method. Fract. Calc. Appl. Anal. 11 2 (2008) 193-202
14. El-Sayed A.M.A., and Gaber M. The Adomian decomposition method for solving partial differential equations of fractal order in finite domains. Phys. Lett. A 359 (2006) 175-182
15. Odibat Z., and Momani S. Approximate solutions for boundary value problems of time-fractional wave equation. Appl. Math. Comput. 181 (2006) 767-774
16. Daftardar-Gejji V., and Jafari H. An iterative method for solving non linear functional equations. J. Math. Anal. Appl. 316 (2006) 753-763
17. Bhalekar S., and Daftardar-Gejji V. New iterative method: Application to partial differential equations. Appl. Math. Comput. 203 (2008) 778-783
18. Lesnic D. A computational algebraic investigation of the decomposition method for time-dependent problems. Appl. Math. Comput. 119 (2001) 197-206
19. Lesnic D. The Cauchy problem for the wave equation using the decomposition method. Appl. Math. Lett. 15 (2002) 697-701