On the initial-boundary-value problem for the time-fractional diffusion equation on the real positive semiaxis (Q274770)

Summary: We consider the time-fractional derivative in the Caputo sense of order \(\alpha \in (0, 1)\). Taking into account the asymptotic behavior and the existence of bounds for the Mainardi and the Wright function in \(\mathbb{R}^+\), two different initial-boundary-value problems for the time-fractional diffusion equation on the real positive semiaxis are solved. Moreover, the limit when \(\alpha \nearrow 1\) of the respective solutions is analyzed, recovering the solutions of the classical boundary-value problems when \(\alpha = 1\), and the fractional diffusion equation becomes the heat equation.