Fractional Calculus

The following sections are included:

• The Fourier transform

• The fractional integral

  • The Liouville fractional integral

  • The Riemann fractional integral

• Correlation of fractional integration and differentiation

  • The Liouville fractional derivative

  • The Riemann fractional derivative

  • The Liouville fractional derivative with inverted operator sequence - the Liouville-Caputo fractional derivative

  • The Riemann fractional derivative with inverted operator sequence - the Caputo fractional derivative

• Fractional derivative of second order

  • The Riesz fractional derivative

  • The Feller fractional derivative

• Fractional derivatives of higher orders - the Marchaud fractional derivative

• Erdélyi-Kober operators of fractional integration

• Geometric interpretation of the fractional integral

• Low level fractionality

• Discussion

  • Semi-group property of the fractional integral