AXIS-SYMMETRIC FRACTIONAL DIFFUSION-WAVE PROBLEM: PART I-ANALYSIS

Abstract: 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 sub-jected to external excitation. We define the problem in terms of Riemann-Liouville fractional derivatives and use modal analysis approach to reduce the continuum prob-lem to a countable infinite degrees-of-freedom problem for which solution could be found in closed form. Here we use Grünwald-Letnikov approximation to find a nu-merical 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 dif-fusion in 2-dimension to axis symmetric case. Key word