Root
/
Conference Proceedings
/
6th EUROMECH Nonlinear Dynamics Conference (ENOC 2008)
/
Axis-symmetric fractional diffusion-wave problem: Part I-Analysis
/

This is part I of a two part paper on an

axis-symmetric fractional diffusion-wave problem. In this part we focus on the response of the system subjected to external excitation. We define the problem in terms of Riemann-Liouville fractional derivatives and use modal analysis approach to reduce the continuum problem to a countable infinite degrees-of-freedom problem for which

solution could be found in closed form. Here we use

Gr\"{u}nwald-Letnikov approximation to find a numerical solution to the problem. This will allow us to solve axis-symmetric fractional optimal control problems which could not be solved in closed form. We validate the scheme by comparing the numerical results with the analytical solutions. The formulation and the approach presented here extends

our earlier work on fractional diffusion in 2-dimension

to axis symmetric case.

axis-symmetric fractional diffusion-wave problem. In this part we focus on the response of the system subjected to external excitation. We define the problem in terms of Riemann-Liouville fractional derivatives and use modal analysis approach to reduce the continuum problem to a countable infinite degrees-of-freedom problem for which

solution could be found in closed form. Here we use

Gr\"{u}nwald-Letnikov approximation to find a numerical solution to the problem. This will allow us to solve axis-symmetric fractional optimal control problems which could not be solved in closed form. We validate the scheme by comparing the numerical results with the analytical solutions. The formulation and the approach presented here extends

our earlier work on fractional diffusion in 2-dimension

to axis symmetric case.