Fractional models, non-locality, and complex systems

Computers and Mathematics with Applications

Volumn 59, Issue 3, 2010, Pages 1048-1056

  Luchko, Yury F ^a   Rivero, Margarita ^b   Trujillo, Juan J ^b   Velasco, M Pilar ^c  

^a BEUTH UNIVERSITY OF APPLIED SCIENCES   (Germany)

^b UNIVERSIDAD DE LA LAGUNA   (Spain)

^c UNIVERSIDAD COMPLUTENSE DE MADRID   (Spain)

Author keywords

Caputo fractional derivative; Complex processes; Deterministic fractional models; Dynamical systems; Fractional differential equations; Population dynamics

Indexed keywords

CAPUTO FRACTIONAL DERIVATIVES; COMPLEX PROCESSES; DETERMINISTIC FRACTIONAL MODELS; FRACTIONAL DIFFERENTIAL EQUATIONS; FRACTIONAL MODEL;

DIFFERENTIAL EQUATIONS; DYNAMICAL SYSTEMS; INVERSE PROBLEMS; POPULATION DYNAMICS;

DYNAMICS;

EID: 74149086307     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2009.05.018     Document Type: Article

References (10)

1. Metzler R., and Klafter J. The random walk's guide to anomalous diffusion: A fractional dynamics approach. Phys. Rep. 339 1 (2000) 1-77
2. Kilbas A.A., Srivastava H.M., and Trujillo J.J. Theory and Applications of Fractional Differential Equations (2006), Elsevier, Amsterdam
3. Bonilla B., Rivero M., Rodríguez-Germá L., and Trujillo J.J. Fractional differential equations as alternative models to nonlinear differential equations. Appl. Math. Comput. 187 (2007) 79-88
4. Luchko Yu., and Gorenflo R. An operational method for solving fractional differential equations with the Caputo derivatives. Acta Math. Vietnam. 24 (1999) 207-233
5. J. Trujillo, L. Vazquez, P. Velasco, Fractional dynamic of populations, Electron. J. Differential Equations (in press)
6. Diethelm K., Ford N., Freed A., and Luchko Yu. Algorithms for the fractional calculus: A selection of numerical methods. Comput. Methods Appl. Mech. Engrg. 194 (2005) 743-773
7. Brunner H. Discretization of Volterra integral equations of the first kind. Math. Comput. 31 (1977) 708-716
8. Brunner H., and van der Houwen P. The Numerical Solution of Volterra Equations (1986), Wiley, Amsterdam
9. Kythe P., and Puri P. Computational Methods for Linear Integral Equations (2002), Birkhäuser, Boston
10. Lamm P. A survey of regularization methods for first-kind Volterra equations. In: Colton D., Engl H.W., Louis A., McLaughlin J.R., and Rundell W. (Eds). Surveys on Solution Methods for Inverse Problems (2000), Springer, New York 53-82