Time-Fractional Diffusion-Wave Equation with Mass Absorption in a Sphere under Harmonic Impact

Abstract

The time-fractional diffusion equation with mass absorption in a sphere is considered under harmonic impact on the surface of a sphere. The Caputo time-fractional derivative is used. The Laplace transform with respect to time and the finite sin-Fourier transform with respect to the spatial coordinate are employed. A graphical representation of the obtained analytical solution for different sets of the parameters including the order of fractional derivative is given.

Keywords

• fractional calculus
• mass absorption
• diffusion-wave equation
• Caputo derivative
• harmonic impact
• Laplace transform
• Fourier transform
• Mittag-Leffler function