Fractional Calculus and Its Applications

Inhaltsverzeichnis

• A brief history and exposition of the fundamental theory of fractional calculus.
• The use in mathematical physics of Erdélyi-Kober operators and of some of their generalizations.
• The weyl fractional calculus.
• H-R transform in two dimensions and some of its applications to partial differential equations.
• Inequalities via fractional integration.
• An access to fractional differentiation via fractional difference quotients.
• A family of integral representations for the solution of the diffusion equation.
• Fractional integrals of generalized functions.
• The fractional derivative and entire functions.
• Formulas of the dirichlet-mehler type.
• A child's garden of special functions.
• An algebraic definition of fractional differentiation.
• Generalized poisson integrals and regularity of functions.
• Fractional spaces of temperate distribution.
• Applications of fractional calculus to spherical (radial) probability models and generalizations.
• A problem of hyperstereology.
• A hypergeometric integral equation.
• Application of fractional differentiation to the modeling of hodograph linearities.
• Fractional calculus in the operator field of generalized functions.
• A functional relation.
• On moments of probability distribution functions.
• Fractional integration of fundamental solutions.
• Fundamental properties of fractional derivatives via pochhammer integrals.
• On the recent trends in the development, theory and applications of fractional calculus.
• Open questions for research.