The Fractional Laplacian

• Presents the material at a level suitable for a broad audience of scientists and engineers with rudimentary background in ordinary differential equations and integral calculus
• Clarifies the concept of the fractional Laplacian for functions in one, two, three, or an arbitrary number of dimensions defined over the entire space, satisfying periodicity conditions, or restricted to a finite domain
• Covers physical and mathematical concepts as well as detailed mathematical derivations
• Develops a numerical framework for solving differential equations involving the fractional Laplacian and presents specific algorithms accompanied by numerical results in one, two, and three dimensions
• Discusses viscous flow and physical examples from scientific and engineering disciplines

Written by a prolific author well known for his contributions in fluid mechanics, biomechanics, applied mathematics, scientific computing, and computer science, the book emphasizes fundamental ideas and practical numerical computation. It includes original material and novel numerical methods.