Analytical and numerical solutions for the time and space-symmetric fractional diffusion equation

We consider a time and space-symmetric fractional diffusion equation (TSS-FDE) under homogeneous Dirichlet conditions and homogeneous Neumann conditions. The TSS-FDE is obtained from the standard diffusion equation by replacing the first-order time derivative by a Caputo fractional derivative, and the second order space derivative by a symmetric fractional derivative. First, a method of separating variables expresses the analytical solution of the TSS-FDE in terms of the Mittag--Leffler function. Second, we propose two numerical methods to approximate the Caputo time fractional derivative: the finite difference method; and the Laplace transform method. The symmetric space fractional derivative is approximated using the matrix transform method. Finally, numerical results demonstrate the effectiveness of the numerical methods and to confirm the theoretical claims.

Analytical and numerical solutions for the time and space-symmetric fractional diffusion equation

We consider a time and space-symmetric fractional diffusion equation (TSS-FDE) under homogeneous Dirichlet conditions and homogeneous Neumann conditions. The TSS-FDE is obtained from the standard diffusion equation by replacing the first-order time derivative by the Caputo fractional derivative and the second order space derivative by the symmetric fractional derivative. Firstly, a method of separating variables is used to express the analytical solution of the tss-fde in terms of the Mittag–Leffler function. Secondly, we propose two numerical methods to approximate the Caputo time fractional derivative, namely, the finite difference method and the Laplace transform method. The symmetric space fractional derivative is approximated using the matrix transform method. Finally, numerical results are presented to demonstrate the effectiveness of the numerical methods and to confirm the theoretical claims.

Elements of public asset management framework for local governments in developing countries

There is a widespread recognition to the need of better manage municipal property in most cities in the world. Structural problems across regional, state, and territorial governments that have legal powers to own and maintain real property are similar, regardless of the level of development of each country. Start from a very basic level of property inventory records. The need for better manage to the local government owned property is the result of widespread decentralisation initiatives that often have devolved huge property portfolios from central to local governments almost “overnight”. At the same time municipal or regional governments were and continue to be unprepared to deal with multiple issues related to the role of property owners and managers. The lack of discussion of public asset management especially the elements that should be incorporated in the framework creates an important challenge to study the discipline of public asset management further. The aim of this paper is to study the practices of public asset management in developed countries, especially the elements of public asset management framework, and its transferability to developing countries. A case study was selected and conducted to achieve this aim. They involved interviews and a focus group. The study found that in public asset management framework, proper asset identification, public asset needs analysis, asset life cycle and performance measurements are an important element that should be incorporated in the framework. Those elements are transferable and applicable to developing countries’ local governments. Finally, findings from this study provide useful input for the local government policy makers, scholars and asset management practitioners to establish a public asset management framework toward more efficient and effective local governments in managing their assets as well as increasing public services quality.