Fractional calculus and applications to stochastic processes. Lecture 1

 Introduction to fractional calculus

• The Riemann-Liouville integral.
• The Riemann-Liouville derivative.
• Relationship between fractional derivative and fractional integral and between fractional integral and fractional derivative.
• The Marchaud derivative.
• Laplace transform of fractional derivative.
• Dzhrbashyan-Caputo derivative.
• Laplace transform of the Dzhrbashyan-Caputo derivative.