Bertram Ross (auth.), Prof. Dr. Bertram Ross (eds.)9780387071619, 0-387-07161-X
Table of contents :
A brief history and exposition of the fundamental theory of fractional calculus….Pages 1-36
The use in mathematical physics of Erdélyi-Kober operators and of some of their generalizations….Pages 37-79
The weyl fractional calculus….Pages 80-89
H-R transform in two dimensions and some of its applications to partial differential equations….Pages 91-105
Inequalities via fractional integration….Pages 106-115
An access to fractional differentiation via fractional difference quotients….Pages 116-145
A family of integral representations for the solution of the diffusion equation….Pages 146-150
Fractional integrals of generalized functions….Pages 151-170
The fractional derivative and entire functions….Pages 171-206
Formulas of the dirichlet-mehler type….Pages 207-215
A child’s garden of special functions….Pages 216-225
An algebraic definition of fractional differentiation….Pages 226-231
Generalized poisson integrals and regularity of functions….Pages 232-248
Fractional spaces of temperate distribution….Pages 249-255
Applications of fractional calculus to spherical (radial) probability models and generalizations….Pages 256-266
A problem of hyperstereology….Pages 267-271
A hypergeometric integral equation….Pages 272-288
Application of fractional differentiation to the modeling of hodograph linearities….Pages 289-293
Fractional calculus in the operator field of generalized functions….Pages 294-297
A functional relation….Pages 298-305
On moments of probability distribution functions….Pages 306-316
Fractional integration of fundamental solutions….Pages 317-322
Fundamental properties of fractional derivatives via pochhammer integrals….Pages 323-356
On the recent trends in the development, theory and applications of fractional calculus….Pages 357-375
Open questions for research….Pages 376-381
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