Fractional calculus and non-reflecting boundary conditions in wave propagation

This paper shows why the fractional calculus naturally arises for modeling the reflection of linear and nonlinear waves at an interface through a boundary operator. The construction of such boundary conditions is difficult and requires the use of advanced mathematical analysis theories related to fractional microlocal calculus. Moreover, the numerical approximation of such operators is nontrivial and leads to fundamental problems of numerical analysis and simulation. Finally, we provide an example of application in computational ocean acoustics. © 2008 Lavoisier, Paris.