On Fractional Partial Differential Equations of Diffusion Type with Integral Kernel

The main purpose of this work is to investigate the existence of solution of the fractional partial differential equations of diffusion type with integral kernel. The existence of solutions of the problem with Dirichlet boundary condition is established by using the Leray–Schauder fixed point theorem and Arzela–Ascoli theorem under suitable assumptions. Then, the result is generalized for Neumann boundary condition with the help of Green’s identity.