Some Applications of the Wright Function in Continuum Physics: A Survey

Abstract

The Wright function is a generalization of the exponential function and the Bessel functions. Integral relations between the Mittag–Leffler functions and the Wright function are presented. The applications of the Wright function and the Mainardi function to description of diffusion, heat conduction, thermal and diffusive stresses, and nonlocal elasticity in the framework of fractional calculus are discussed.

Keywords

• fractional calculus
• Caputo derivative
• Mittag–Leffler functions
• Wright function
• Mainardi function
• Laplace transform