Fractional Calculus and Its Applications

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