Analytical Investigation of the Boundary Value Problems for the Generalized Conformable Fractional Diffusion Equations in One Dimension

Abstract In this work, we extend the scope of a recently proposed conformable fractional derivative known as the "generalized fractional derivative" (GFD) to include the one-dimensional fractional linear diffusion equations (heat and wave equations). Their corresponding boundary value problems are solved analytically by means of the separation of variables and Fourier analysis. The obtained solutions are represented graphically to investigate their behavior and accuracy.