Continuous time random walk to a general fractional Fokker–Planck equation on fractal media

A general fractional calculus is described using fractional operators with respect to another function, and some often used propositions are presented in this framework. Together with the continuous time random walk (CTRW), a general time-fractional Fokker–Planck equation is derived and the governing equation meets the general fractional derivative. Finally, various new probability density functions are proposed in this paper.