Table of some basic fractional calculus formulae derived from a modified Riemann-Liouville derivative for non-differentiable functions

Applied Mathematics Letters

Volumn 22, Issue 3, 2009, Pages 378-385

  Jumarie, Guy ^a  

^a UNIVERSITÉ DU QUÉBEC À MONTRÉAL   (Canada)

Author keywords

Fractional calculus; Fractional Taylor's series; Mittag Leffler function; Modified Riemann Liouville derivative

Indexed keywords

CALCULATIONS; DIFFERENTIATION (CALCULUS); PROBABILITY DENSITY FUNCTION;

DIFFERENTIABLE FUNCTIONS; FRACTIONAL CALCULUS; FRACTIONAL CALCULUSES; FRACTIONAL DERIVATIVES; FRACTIONAL ORDERS; FRACTIONAL TAYLOR'S SERIES; MITTAG-LEFFLER FUNCTION; MODIFIED RIEMANN-LIOUVILLE DERIVATIVE; TAYLOR'S SERIES;

DERIVATIVES;

EID: 57049186538     PISSN: 08939659     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.aml.2008.06.003     Document Type: Article

References (24)

1. Al-Akaidi M. Fractal Speech Processing (2004), Cambridge University Press
2. Campos L.MC. On a concept of derivative of complex order with applications to special functions. IMA J. Appl. Math. 33 (1984) 109-133
3. Campos L.M.C. Fractional calculus of analytic and branched functions. In: Kalia R.N. (Ed). Recent Advances in Fractional Calculus (1993), Global Publishing Company
4. Caputo M. Linear model of dissipation whose Q is almost frequency dependent II. Geophys. J. R. Ast. Soc. 13 (1967) 529-539
5. Djrbashian M.M., and Nersesian A.B. Fractional derivative and the Cauchy problem for differential equations of fractional order. Izv. Acad. Nauk Armjanskoi SSR 3 1 (1968) 3-29 (in Russian)
6. Jumarie G. Stochastic differential equations with fractional Brownian motion input. Int. J. Syst. Sc. 24 6 (1993) 1113-1132
7. α. Appl. Math. Lett. 18 (2005) 739-748
8. Jumarie G. On the solution of the stochastic differential equation of exponential growth driven by fractional Brownian motion. Appl. Math. Lett. 18 (2005) 817-826
9. Jumarie G. Modified Riemann-Liouville derivative and fractional Taylor series of non-differentiable functions Further results. Comput. Math. Appl. 51 (2006) 1367-1376
10. Jumarie G. New stochastic fractional models for Malthusian growth, the Poissonian birth prodess and optimal management of populations. Math. Comput. Modelling 44 (2006) 231-254
11. Kober H. On fractional integrals and derivatives. Quart. J. Math. Oxford 11 (1940) 193-215
12. Kolwankar KM., and Gangal AD. Holder exponents of irregular signals and local fractional derivatives. Pramana J. Phys. 48 (1997) 49-68
13. Kolwankar KM., and Gangal AD. Local fractional Fokker-Planck equation. Phys. Rev. Lett. 80 (1998) 214-217
14. Letnikov A.V. Theory of differentiation of fractional order. Math. Sb. 3 (1868) 1-7
15. Liouville J. Sur le calcul des differentielles à indices quelconques. J. Ecole Polytechnique 13 (1832) 71 (in french)
16. Miller K.S., and Ross B. An Introduction to the Fractional Calculus and Fractional Differential Equations (1933), Wiley, New York
17. Nishimoto K. Fractional Calculus (1989), Descartes Press Co., Koroyama
18. Oldham K.B., and Spanier J. The Fractional Calculus. Theory and Application of Differentiation and Integration to Arbitrary Order (1974), Acadenic Press, New York
19. Ortigueira M.D. Introduction to Fractional Signal Processing. Part I: Continuous Time Systems. IEE Proc. Vision Image Signal Process. I (2000) 62-70
20. Osler T.J. Taylor's series generalized for fractional derivatives and applications. SIAM. J. Math. Anal. 2 1 (1971) 37-47
21. Oustaloup A. La derivation non entiere: Theorie, synthese et applications (Non-Integer Derivation: Theory, Synthesis and Applications) (1995), Editions Hermes, Paris (in French)
22. Podlubny I. Fractional Differential Equations (1999), Academic Press, San Diego
23. Ross B. Fractional Calculus and its Applications. Lecture Notes in Mathematics vol. 457 (1974), Springer, Berlin
24. Samko S.G., Kilbas A.A., and Marichev O.I. Fractional Integrals and derivatives. Theory and Applications (1987), Gordon and Breach Science Publishers, London