Fractional radial diffusion equation analytical solution via Hankel and Sumudu transforms

Abstract

In this work we derive the analytical solution for the following fractional radial diffusion equation, $$ D_{t}^{2\alpha }{v}\left( r,\,t\right) \,+2\,a\,D_{\,t}^{\alpha }{v}\left( r,\,t\right) \,\,=\,\,d\left( \frac{\partial ^{2}{v}\left( r,\,t\right) }{% \partial r^{2}}\,+\,\frac{1}{r}{v}\left( r,\,t\right) \right) \,+\,f\left( \,t\right) . $$% The solution is obtained in terms of Fox and Fox-Wright functions{, }by means of Hankel and Sumudu transforms.