Analytical solutions to time-fractional partial differential equations in a two-dimensional multilayer annulus

► Fractional differential equation in a two-dimensional multilayer annulus is studied. ► Solutions are applicable to any combination of inhomogeneous boundary condition. ► Classical diffusion, wave and Helmholtz equation are discussed as special cases. ► An illustrative example problem for the semi-circular annular region is solved. ► Numerical results are presented graphically for various kind of order of α.