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.

Doppler effect described by the solutions of the Cattaneo telegraph equation

“…The quasi-steady-state solutions are also considered for the case of non-moving time-harmonic source and time-harmonic boundary condition for temperature. The paper develops the results of previous authors' investigations [22,[28][29][30][31].…”

A Numerical Calculation of Arbitrary Integrals of Functions

“…In recent years considerable interest in fractional differential equation has been stimulated by the applications that it finds in the field of science, including numerical analysis, engineering, economics, biology, oil industry, finance and others [11] - [20]. Real life modeling of phenomenon having dependence not solely at the time instant, however additionally the previous time history can be successfully achieved by fractional calculus.…”

Axisymmetric Fractional Diffusion with Mass Absorption in a Circle under Time-Harmonic Impact

“…In [ 38 ], the time-fractional diffusion equation with mass absorption and a source term varying harmonically in time was considered in the domain . In [ 39 ], this equation was studied for a sphere. In the present paper, we investigate the axisymmetric time-fractional diffusion equation with mass absorption ( 10 ) in a circle, under the time-harmonic Dirichlet boundary condition.…”