Generalized pathway entropy and its applications in diffusion entropy analysis and fractional calculus

Abstract: We presented background information about various entropies in the literature. The pathway idea of Mathai (2005) is shown to be inferable from the maximization of a certain generalized entropy measure and established connections to outstanding problems in astronomy and physics. In this paper we proved that the generalized entropy of Mathai associated with diffusive processes grows linearly with the logarithm of time, and the rate of growth is indepen- dent of the generalized entropy parameter. We also proposed some results concerning images of generalized Bessel function under the pathway operator and its special cases including some trigonometric functions. Situations are listed where a generalized entropy of order ? leads to pathway models, exponential and power law behavior and related differential equations.