关键词: 分数阶微积分;分形介质;分数阶振子;Laplace变换;有限Hankel变换;广义MittagLeffler函数

Abstract:

he fractional reactiondiffusion differential equation with  a fractional oscillator in  a finite fractal medium was  established. By applying Laplace transformation, the finite Hankel transformation and their inverse transform, the exact solution of the model were obtained. The expression  in the form of the generalized MittagLeffler function was  given. Finally, the solutions of twodimensional space, threedimensional space and the integral diffusion equation as some particular cases of this paper were discussed.

Key words: fractional calculus; fractal medium; fractional oscillator; Laplace transform; the finite Hankel transform; generalized MittagLeffler function