Unified space-time fractional cable equation

Recently fractional cable equation has been investigated by many authors who have applied it in various areas. Here we introduce and investigate a generalized space-time fractional cable equation associated with Riemann-Liouville and Hilfer fractional derivatives. By mainly applying both Laplace and Fourier transforms, we express the solution of the proposed generalized fractional cable equation as H-functions. The main results here are general enough to be specialized to yield many new and known results, only several of which are demonstrated in corollaries. Finally, we consider the moment of the Green function with its several asymptotic formulas.

Keywords:

Space-time fractional cable equation , Riemann-Liouville fractional derivatives , Caputo fractional derivative , Hilfer operator , Mittag-Leffler function , Green function , H-function , Laplace transform , Fourier Transform , Moments of the Green function