Fractional differential equations and their applications

The Laplace transform method for solving fractional differential equations is pre sented. The fractional diffusion and fractional Schrödinger equations together with their properties are investigated. The Lagrangians linear in velocities are analyzed using the fractional calculus, and the fractional Euler-Lagrange equations are derived. Keywords: Fractional derivative, fractional integral, fractional diffusion equation, frac tional Schrödinger equation, fractional Euler-Lagrange equations. Ill