• Bruce J. West
  • Mauro Bologna
  • Paolo Grigolini
Part of the Institute for Nonlinear Science book series (INLS)


The special functions of mathematical physics are those analytic functions that have been of assistance in understanding a variety of physical phenomena. For example, wave propagation in homogeneous and inhomogeneous media, heat transport, diffusion, conduction, and so on. These functions have, by and large, been solutions to partial differential equations that describe the evolution of the physical phenomena of interest. Here we investigate how to generate these functions using fractal operators, see also Bologna[2].


Special Function Fractional Derivative Hypergeometric Function Fractal Operator Laguerre Polynomial 
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  1. [1]
    C. Fox, Trans. Am. Math. Soc. 98, 395 (1910).Google Scholar
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    M. Bologna, Derivata ad Indice Reale, Ets Editrice, Italy (1990).Google Scholar
  3. [3]
    A. M. Mathai and R. K. Saxena, The Fox-Function with Applications in Staistics and Other Disciplines, Wilry Eastern Limited, New Delhi (1978).Google Scholar
  4. [4]
    W. G. Glöckle and T. F. Nonnenmacher, Fox function representation of non-Debye relaxation processes, J. Stat. Phys. 71 (1993) 741.ADSzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag New York, Inc. 2003

Authors and Affiliations

  • Bruce J. West
    • 1
  • Mauro Bologna
    • 2
  • Paolo Grigolini
    • 2
  1. 1.Department of the Army, U.S. Army Research LaboratoryArmy Research OfficeResearch Triangle ParkUSA
  2. 2.Department of PhysicsUniversity of North TexasDentonUSA

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