Solution of a fractional transport equation by using the generalized quadratic form

Communications in Nonlinear Science and Numerical Simulation

Volumn 16, Issue 8, 2011, Pages 3011-3014

  Kadem, Abdelouahab ^a   Baleanu, Dumitru ^b  

^a FERHAT ABBAS UNIVERSITY   (Algeria)

^b CANKAYA UNIVERSITY   (Turkey)

Author keywords

Caputo fractional derivative; Fick's law; Fractional transport equations; Generalized quadratic form

Indexed keywords

DIFFERENTIATION (CALCULUS); NUMBER THEORY;

ANGULAR FLUX; CAPUTO FRACTIONAL DERIVATIVES; FICK'S LAW; FRACTIONAL GENERALIZATION; FRACTIONAL TRANSPORT EQUATION; GENERALIZED QUADRATIC FORM; ONE-DIMENSIONAL; QUADRATIC FORM; SCALAR FLUXES; SOURCE FLUX;

FICK'S LAWS;

EID: 79952536080     PISSN: 10075704     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cnsns.2010.10.032     Document Type: Article

References (19)

1. Kadem A., Baleanu D. Fractional radiative equation within Chebyshev spectral approach. Comput Math Appl 2010, 59(5):1865-1873.
2. Kadem A., Baleanu D. Analytical method based on Walsh function combined with orthogonal polynomial for fractional transport equation. Commun Nonlinnear Sci Numer Simul 2010, 15(3):491-501.
3. Kilbas A.A., Srivastava H.M., Trujillo J.J. Theory and applications of fractional differential equations 2006, vol. 204. North-Holland Mathematics Studies.
4. Podlubny I. Fractional differential equations 1999, Academic Press, San Diego.
5. Samko G, Kilbas AA, Marichev OI. Fractional integrals and derivatives: theory and applications, Gordon and Breach, Yverdon, 1993.
6. Magin R.L. Fractional calculus in bioengineering 2006, Begell House Publisher, Inc., Connecticut.
7. Momani S., Odibat Z. Numerical approach to differential equations of fractional order. J Comput Appl Math 2007, 207:96-121.
8. Kudryashov N.A. Simplest equation method to look for exact solutions of nonlinear differential equations. Chaos Solitons Fract 2005, 24:1217-1231.
9. Tarasov V.E., Zaslavsky G.M. Conservation laws and Hamilton's equations for systems with long-range interaction and memory. Commun Nonlinear Sci Numer Simul 2008, 13(9):1860-1878.
10. Jesus I.S., Machado J.A.T. Fractional control of heat diffusion systems. Nonlinear Dyn 2008, 54(3):263-282.
11. Magin R.L., Feng X., Baleanu D. Solving the fractional order Bloch equation. Concept Mag Reson Part A 2009, 34A(1):16-25.
12. Couceiro M.S., Ferreira N.M.F., Machado J.A.T. Application of fractional algorithms in the control of a robotic bird. Commun Nonlinear Sci Numer Simul 2010, 15(4):895-910.
13. Scalas E., Gorenflo R., Mainardi F. Uncoupled continuous-time random walks: solution and limiting behavior of the master equation. Phys Rev E 2004, 69:011107-1.
14. Golmankhaneh A.K., Golmankhaneh A.K., Baleanu D., Baleanu M.C. Hamiltonian structure of fractional first order Lagrangian. Int J Theor Phys 2010, 49(2):365-375.
15. Muslih S.I., Agrawal O.P., Baleanu D. A fractional Dirac equation and its solution. J Phys A-Math Theor 2010, 43(5). Article Number: 055203.
16. Schneider W.R., Wyss W. Fractional diffusion and wave equations. J Math Phys 1989, 30:134-144.
17. Baleanu D., Muslih S.I. Lagrangian formulation of classical fields within Riemann-Liouville fractional derivatives. Phys Scripta 2005, 72(2-3):119-121.
18. Rabei E.M., Nawafleh K.I., Hijjawi R.S., Muslih S.I., Baleanu D. The Hamilton formalism with fractional derivatives. J Math Anal Appl 2007, 327:891-897.
19. Larsen EW. Infinite medium solutions of the transport equation, SN discretization schemes, and the diffusion approximation. M&C 2001 Salt Lake City, Utah, USA, September, 2001.