Pathway to Fractional Integrals, Fractional Differential Equations and the Role of H-function

The pathway model for the real scalar variable case is re-explored and its connections to fractional integrals, solutions of fractional differential equations, Tsallis statistics and superstatistics in statistical mechanics, reaction-rate probability integral, Kraetzel transform, and pathway transform are explored. It is shown that the common thread in these connections is the H-function representations. The pathway parameter is shown to be connected to the fractional order in fractional integrals and fractional differential equations.