Maryam Mohammadi

Maryam Mohammadi, Robert Schaback

The paper provides the fractional integrals and derivatives of the Rie\-mann-Liouville and Caputo type for the five kinds of radial basis functions (RBFs), including the powers, Gaussian, multiquadric, Matern and thin-plate splines, in one dimension. It allows to use high order numerical methods for solving fractional differential equations. The results are tested by solving two fractional differential equations. The first one is a fractional ODE which is solved by the RBF collocation method and the second one is a fractional PDE which is solved by the method of lines based on the spatial trial spaces spanned by the Lagrange basis associated to the RBFs.

Maryam Mohammadi, Masine Md. Tap

This paper addresses a mixed integer programming (MIP) formulation for the multi-item uncapacitated lot-sizing problem that is inspired from the trailer manufacturer. The proposed MIP model has been utilized to find out the optimum order quantity, optimum order time, and the minimum total cost of purchasing, ordering, and holding over the predefined planning horizon. This problem is known as NP-hard problem. The model was presented in an optimal software form using LINGO 13.0.