Fractional Diffusion Equations and Special Functions

Fractional calculus provides powerful mathematical tools for modeling anomalous transport, non-local behavior, and memory effects across modern physics and engineering. This course introduces you to the core mathematics of fractional diffusion equations in a step-by-step, text-based format. You will build a solid understanding of how fractional derivatives extend classical calculus and learn how to solve real-world fractional differential equations using essential special functions. What you'll learn: - Understand the core principles and definitions of fractional derivatives and integrals - Master the properties and applications of the Mittag-Leffler function family - Explore Wright functions and their role in fundamental solutions - Solve fractional diffusion equations using Laplace and Fourier transform techniques - Model anomalous diffusion phenomena and interpret physical behavior analytically - Apply numerical approximations and modern computational perspectives to fractional systems The course begins with foundational terminology, standard differential models, and fractional integral definitions before advancing to analytical solutions, special function properties, and practical modeling exercises. This course is designed for students, researchers, and engineers who want an approachable, foundational introduction to fractional differential equations. Start reading to master the mathematics of fractional diffusion.