Volterra-Prabhakar function of distributed order and some applications

The paper studies the exact solution of two kinds generalized Fokker-Planck equations in which integral kernels are given either by distributed order function $k_{1}(t) = \int_{0}^{1} t^{-\mu}/\Gamma(1- \mu) d\mu$ or Prabhakar $k_{2}(\alpha, \gamma; \lambda; t) e^{-\gamma}_{\alpha, 1 - \mu}(\lambda; d\mu$, where is denoted as $e^{-\gamma}_{\alpha, t)$. Both these can be called fading memory functions and Stieltjes functions. It also shown that their character enough to ensure non-negativity mean square values higher even moments. odd moments vanish. Thus, probability density We introduce Volterra-Prabhakar its generalization involved definition t)$ generated it $p_2(x,