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.
Highlights
IntroductionApplications of the Wright Function in Continuum Physics: A Survey
In the present survey article, we briefly discuss the properties of the Mittag–Leffler functions and Wright function and present the integral relations between the Mittag–Leffler functions and the Wright function
We have reviewed the main applications of the Wright function and the Mainardi function in continuum physics based essentially on the author’s works
Summary
Applications of the Wright Function in Continuum Physics: A Survey. The Mittag–Leffler functions and the Wright function appear in solutions of various types of equations with fractional operators. The. Wright function was presented in [27,28] and later on discussed by Erdélyi–Magnus–. In 1996, Mainardi [31,32] solved the diffusion-wave equation with the Caputo fractional derivative of the order α. In the present survey article, we briefly discuss the properties of the Mittag–Leffler functions and Wright function and present the integral relations between the Mittag–. The applications of the Wright function and the Mainardi function to the description of diffusion, heat conduction, thermal and diffusive stresses, and nonlocal elasticity in the framework of fractional calculus are reviewed
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