With the aid of symbolic computation, the sinh-Gordon equation expansion method is extended to seek Jacobi elliptic function solutions of (2+1)-dimensional long wave-short wave resonance interaction equation, which describe the long and short waves propagation at an angle to each other in a two-layer fluid. As a result, new Jacobi elliptic function solutions are obtained. When the modulus m of ...

In this paper, operational matrices of Riemann-Liouville fractional integration and Caputo fractional differentiation for shifted Jacobi polynomials are considered. Using the given initial conditions, we transform the fractional differential equation (FDE) into a modified fractional differential equation with zero initial conditions. Next, all the existing functions in modified differential equ...

In this paper, a Jacobi-collocation spectral method is developed for Volterra integral equations of second kind with a weakly singular kernel. We use some function transformation and variable transformations to change the equation into a new Volterra integral equation defined on the standard interval [−1, 1], so that the solution of the new equation possesses better regularity and the Jacobi or...

Using the “basic monotonicity property” along locally admissible trajectories, we extend to very general problems certain existing results concerning the differential inequalities verified by the value function of an optimal control problem; these differential inequalities are expressed in terms of its contingent, quasitangent, and peritangent (Clarke’s) directional derivatives and in terms of ...

Abstract. In this paper, the solvability of a class of forward-backward stochastic di erential equations (SDEs for short) over an arbitrarily prescribed time duration is studied. We design a stochastic relaxed control problem, with both drift and di usion all being controlled, so that the solvability problem is converted to a problem of nding the nodal set of the viscosity solution to a certain...

Private sector operators of response services such as ambulance, fire or police etc. are often regulated by targets on the distribution of response times. This may result in inefficient overstaffing to ensure those targets are met. In this paper, we use a network chain of M/M/K queues to model the arrival and completion of jobs on the system so that quantities such as the expected total time wa...

This paper deals with the optimal control of a stochastic delay differential equation arising in the management of a pension fund with surplus. The problem is approached by the tool of the representation in infinite dimension. We show the equivalence between the 1-dimensional delay problem and the associated infinite dimensional problem without delay. Then we prove that the value function is co...

In this paper we analyze a Boltzmann type mean field game model for knowledge growth, which was proposed by Lucas and Moll [14]. We discuss the underlying mathematical model, which consists of a coupled system of a Boltzmann type equation for the agent density and a Hamilton-Jacobi-Bellman equation for the optimal strategy. We study the analytic features of each equation separately and show loc...

Abstract. The Symplectic Pontryagin method was introduced in a previous paper. This work shows that this method is applicable under less restrictive assumptions. Existence of solutions to the Symplectic Pontryagin scheme are shown to exist without the previous assumption on a bounded gradient of the discrete dual variable. The convergence proof uses the representation of solutions to a Hamilton...

In statistical control, the cost function is viewed as a random variable and one optimizes the distribution of the cost function through the cost cumulants. We consider a statistical control problem for a control-affine nonlinear system with a nonquadratic cost function. Using the Dynkin formula, the Hamilton–Jacobi–Bellman equation for the nth cost moment case is derived as a necessary conditi...