Fractional evolution Dirac-like equations: Some properties and a discrete Von Neumann-type analysis

Journal of Computational and Applied Mathematics

Volumn 224, Issue 1, 2009, Pages 284-295

  Pierantozzi, Teresa ^a  

^a UNIVERSIDAD COMPLUTENSE DE MADRID   (Spain)

Author keywords

Finite difference methods; Fractional derivatives and integrals; Special functions; Stability of numerical methods

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; DIFFERENTIAL EQUATIONS; DIFFERENTIATION (CALCULUS); MATHEMATICAL OPERATORS; NUMERICAL METHODS; SOUND REPRODUCTION; SYSTEM STABILITY;

ANALYTICAL METHODS; ANALYTICAL PROPERTIES; DISCRETE SCHEMES; DISCRETIZATIONS; EVOLUTION EQUATIONS; FINITE DIFFERENCE METHODS; FRACTIONAL CALCULUSES; FRACTIONAL DERIVATIVES AND INTEGRALS; FRACTIONAL DIFFERENTIAL OPERATORS; GENERAL SOLUTIONS; INTEGER ORDERS; LOCAL PROPERTIES; NEUMANN; NUMERICAL SCHEMES; SPACE DIMENSIONS; SPECIAL FUNCTIONS; SYSTEM OF EQUATIONS; TYPE ANALYSIS;

WAVE EQUATIONS;

EID: 56449094573     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2008.05.032     Document Type: Article

References (22)

1. Caputo M. Linear models of dissipation whose Q is almost frequency independent. II. Geophys. J. R. Astr. Soc. 13 (1967) 529-539
2. Diethelm K. An algorithm for the numerical solution of differential equations of fractional order. Elect. Transact. Numer. Anal. 5 (1997) 1-6
3. Erdelyi A., Magnus W., Oberhettinger F., and Tricomi F.G. Higher Transcendental Functions vol. 3 (1953), McGraw-Hill Book Corp., New York
4. Hilfer R. Applications of Fractional Calculus in Physics (2000), World Scientific, New Jersey
5. Kilbas A.A., Pierantozzi T., Trujillo J., and Vázquez L. On the solution of fractional evolution equations. J. Phys. A: Math. Gen. 37 (2004) 3271-3283
6. Lubich Ch. Convolution quadrature and discretized operational calculus. Numer. Math. 52 (1988) 129-145 413-425
7. Mainardi F., and Tomirotti M. On a special function arising in the time fractional diffusion-wave equation. In: Rusev P., Dimovski I., and Kiryakova V. (Eds). Transform Methods and Special Functions, Sofia, 1994 (1995), Science Culture Technology, Singapore 171-183
8. Mainardi F. On the initial value problem for the fractional diffusion-wave equation. Waves and Stability in Continuous Media, Bologna, 1993. Ser. Adv. Math. Appl. Sci. 23 (1994) 246-251
9. Metzler R., and Klafter J. The random Walk's guide to anomalous diffusion: A fractional dynamics approach. Phys. Reports 339 (2000) 1-77
10. Metzler R., and Nonnemacher T.F. Space- and time-fractional diffusion and wave equations, fractional Fokker-Planck equations, and physical motivation. Chem. Phys. 284 1-2 (2002) 67-90
11. Oldham K.B., and Spanier J. The replacement of Fick's laws by a formulation involving semidifferentiation. J. Electroanalyt. Chem. 26 (1970) 331-341
12. Pierantozzi T., and Vázquez L. An interpolation between the wave and diffusion equations through the fractional evolution equations Dirac like. J. Math. Phys. 46 (2005) 113512-113523
13. Pierantozzi T., and Vázquez L. A numerical study of fractional evolution-diffusion Dirac like equations. In: Topping B.H.V., Montero G., and Montenegro R. (Eds). Proceedings of the Fifth International Conference on Engineering Computational Technology, Gran Canaria, Spain, 12-15/09/06 (2006), Civil-Comp Press, Stirlingshire, Scotland 43-44
14. Podlubny I. Fractional Differential Equations. Mathematics in Science and Engineering. 198 (1999), Academic Press, San-Diego
15. Samko S.G., Kilbas A.A., and Marichev O.I. Fractional Integrals and Derivatives. Theory and Applications (1993), Gordon and Breach, Yverdon
16. Schneider W.R., and Wyss W. Fractional diffusion and wave equations. J. Math. Phys. 30 (1989) 134-144
17. Schweber S.S. An Introduction to Relativistic Quantum Field Theory (1966), Harper Int. Ed, New York
18. Thomas J.W. Numerical Partial Differential Equations: Finite Difference Methods. Texts in Applied Mathematics vol. 22 (1995), Springer-Verlag, New York
19. Thomas J.W. Numerical Partial Differential Equations: Conservation Laws and Elliptic Equations. Texts in Applied Mathematics vol. 33 (1999), Springer-Verlag, New York
20. Vázquez L. Fractional diffusion equation with internal degrees of freedom. J. Comp. Math. 21 4 (2003) 491-494
21. Vázquez L., and Jiménez S. Dispersion Relations. Encyclopedia of Nonlinear Science NL3301 (2005) 222-223
22. Vázquez L., and Vilela Mendes R. Fractionally coupled solutions of the diffusion equation. Appl. Math. Comp. 141 (2003) 125-130