A new numerical technique for solving the local fractional diffusion equation: Two-dimensional extended differential transform approach

Applied Mathematics and Computation

Volumn 274, Issue , 2016, Pages 143-151

  Yang, Xiao Jun ^a   Tenreiro Machado, J A ^b   Srivastava, H M ^c,d  

^a CHINA UNIVERSITY OF MINING AND TECHNOLOGY   (China)

^b INSTITUTO SUPERIOR DE ENGENHARIA DO PORTO   (Portugal)

^c UNIVERSITY OF VICTORIA   (Canada)

^d CHINA MEDICAL UNIVERSITY   (Taiwan)

Author keywords

Diffusion equation; Extended differential transform method; Local fractional derivatives; Numerical solution; Partial differential equations

Indexed keywords

COMPUTATION THEORY; DIFFUSION; PARTIAL DIFFERENTIAL EQUATIONS;

COMPUTATIONAL TECHNIQUE; DIFFERENTIAL TRANSFORM; DIFFERENTIAL TRANSFORM METHOD; DIFFUSION EQUATIONS; FRACTIONAL DIFFUSION EQUATION; LOCAL FRACTIONAL DERIVATIVES; NUMERICAL SOLUTION; NUMERICAL TECHNIQUES;

NUMERICAL METHODS;

EID: 84947277335     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2015.10.072     Document Type: Article

References (30)

1. A.A. Kilbas, H.M. Srivastava, and J.J. Trujillo Theory and Applications of Fractional Differential Equations North-Holland Mathematical Studies vol. 204 2006 Elsevier (North-Holland) Science Publishers Amsterdam, London and New York
2. V.E. Tarasov Fractional Dynamics: Applications of Fractional Calculus to Dynamics of Particles, Fields and Media 2011 Springer Berlin, Heidelberg and New York
3. J. Sabatier, O.P. Agrawal, and J.A.T. Machado Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering 2007 Springer Berlin, Heidelberg and New York
4. Y. Zhou Basic Theory of Fractional Differential Equations 2014 World Scientific Publishing Company Singapore, New Jersey, London and Hong Kong
5. D. Baleanu, and O.G. Mustafa Asymptotic Integration and Stability: For Ordinary, Functional and Discrete Differential Equations of Fractional Order Series on Complexity, Nonlinearity and Chaos vol. 4 2015 World Scientific Publishing Company Singapore, New Jersey, London and Hong Kong
6. H. Jafari, and V. Daftardar-Gejji Solving linear and nonlinear fractional diffusion and wave equations by Adomian decomposition Appl. Math. Comput. 180 2006 488 497
7. S. Das Analytical solution of a fractional diffusion equation by variational iteration method Comput. Math. Appl. 57 2009 483 487
8. S. Abbasbandy, and A. Shirzadi Homotopy analysis method for multiple solutions of the fractional Sturm-Liouville problems Numer. Algorithm 54 2010 521 532
9. W. Chen, L. Ye, and H. Sun Fractional diffusion equations by the Kansa method Comput. Math. Appl. 59 2010 1614 1620
10. M. Zayernouri, and G.E. Karniadakis Discontinuous spectral element methods for time-and space-fractional advection equations SIAM J. Sci. Comput. 36 2014 B684 B707
11. E.H. Doha, A.H. Bhrawy, and S.S. Ezz-Eldien A Chebyshev spectral method based on operational matrix for initial and boundary value problems of fractional order Comput. Math. Appl. 62 2011 2364 2373
12. F. Liu, M.M. Meerschaert, R.J. McGough, P.-H. Zhuang, and Q.-X. Liu Numerical methods for solving the multi-term time-fractional wave-diffusion equation Fract. Calc. Appl. Anal. 16 2013 9 25
13. K. Diethelm, N.J. Ford, A.D. Freed, and Y.F. Luchko Algorithms for the fractional calculus: a selection of numerical methods Comput. Methods Appl. Mech. Eng. 194 2005 743 773
14. A. Hanyga Multidimensional solutions of space-fractional diffusion equations Proc. R. Soc. Lond. Ser. A 457 2001 2993 3005
15. A. Arikoglu, and I. Ozkol Solution of fractional differential equations by using differential transform method Chaos Solitons Fractals 34 2007 1473 1481
16. Z. Odibat, and S. Momani A generalized differential transform method for linear partial differential equations of fractional order Appl. Math. Lett. 21 2008 194 199
17. M. Kurulay, and M. Bayram Approximate analytical solution for the fractional modified KdV by differential transform method Commun. Nonlinear Sci. Numer. Simul. 15 2010 1777 1782
18. A. Al-Rabtah, V.S. Ertürk, and S. Momani Solutions of a fractional oscillator by using differential transform method Comput. Math. Appl. 59 2010 1356 1362
19. J. Liu, and G. Hou Numerical solutions of the space- and time-fractional coupled Burger's equations by generalized differential transform method Appl. Math. Comput. 217 2011 7001 7008
20. X.-J. Yang Advanced Local Fractional Calculus and Its Applications 2012 World Science Publisher New York, London and Hong Kong
21. K.M. Kolwankar, and A.D. Gangal Local fractional Fokker-Planck equation Phys. Rev. Lett. 80 1998 214
22. A. Carpinteri, B. Chiaia, and P. Cornetti Static-kinematic duality and the principle of virtual work in the mechanics of fractal media Comput. Methods Appl. Mech. Eng. 191 2001 3 19
23. C. Cattani, H.M. Srivastava, and X.-J. Yang Fractional Dynamics 2015 Emerging Science Publishers (De Gruyter Open) Berlin and Warsaw
24. D. Baleanu, J.A.T. Machado, C. Cattani, M.C. Baleanu, and X.-J. Yang Local fractional variational iteration and decomposition methods for wave equation on Cantor sets within local fractional operators Abstr. Appl. Anal. 2014 2014 1 6
25. Y.-J. Yang, and L.-Q. Hua Variational iteration transform method for fractional differential equations with local fractional derivative Abstr. Appl. Anal. 2014 2014 1 9
26. J.-H. He A tutorial review on fractal space-time and fractional calculus Int. J. Theor. Phys. 53 11 2014 3698 3718
27. X.-J. Yang, H.M. Srivastava, and C. Cattani Local fractional homotopy perturbation method for solving fractal partial differential equations arising in mathematical physics Rom. Rep. Phys. 67 2015 752 761
28. A. Carpinteri, B. Chiaia, and P. Cornetti The elastic problem for fractal media: basic theory and finite element formulation Comput. Struct. 82 2004 499 508
29. X.-J. Yang, D. Baleanu, and H.M. Srivastava Local fractional similarity solution for the diffusion equation defined on cantor sets Appl. Math. Lett. 47 2015 54 60
30. X.-J. Yang, and H.M. Srivastava An asymptotic perturbation solution for a linear oscillator of free damped vibrations in fractal medium described by local fractional derivatives Commun. Nonlinear Sci. Numer. Simul. 29 2015 499 504