In this paper, we apply spectral method based on the Bernstein polynomials for solving a class of optimal control problems with Jumarie’s modified Riemann-Liouville fractional derivative. In the first step, we introduce the dual basis and operational matrix of product based on the Bernstein basis. Then, we get the Bernstein operational matrix for the Jumarie’s modified Riemann-Liouville fractio...

Given an n-vertex graph G, the matrix Ω(G) = (In + L(G))−1 = (ωij) is called the doubly stochastic graph matrix of G, where In is the n × n identity matrix and L(G) is the Laplacian matrix of G. Let ω(G) be the smallest element of Ω(G). Zhang and Wu [X.D. Zhang and J.X. Wu. Doubly stochastic matrices of trees. Appl. Math. Lett., 18:339–343, 2005.] determined the tree T with the minimum ω(T ) am...

Operational risks are defined as risks of human origin. Unlike financial risks that can be handled in a financial manner (e.g. insurances, savings, derivatives), the treatment of operational risks calls for a “managerial approach”. Consequently, we propose a new way of dealing with operational risk, which relies on the well known aggregate planning model. To illustrate this idea, we have adapte...

Operational risks are defined as risks of human origin. Unlike financial risks that can be handled in a financial manner (e.g. insurances, savings, derivatives), the treatment of operational risks calls for a “managerial approach”. Consequently, we propose a new way of dealing with operational risk, which relies on the well known aggregate planning model. To illustrate this idea, we have adapte...

Stochastic fractional differential equations (SFDEs) have many physical applications in the fields of turbulance, heterogeneous, flows and matrials, viscoelasticity and electromagnetic theory. In this paper, a new wavelet Galerkin method is proposed for numerical solution of SFDEs. First, fractional and stochastic operational matrices for the Chebyshev wavelets are introduced. Then, these opera...

We present a transformation for stochastic matrices and analyze the effects of using it in stochastic comparison with the strong stochastic (st) order. We show that unless the given stochastic matrix is row diagonally dominant, the transformed matrix provides better st bounds on the steady state probability distribution.