Integral transform methods are widely used to solve the several dynamic equations with initial values or boundary conditions which are represented by integral equations. With this purpose, the Sumudu transform is introduced in this article as a new integral transform on a time scale T to solve a system of dynamic equations. The Sumudu transform on time scale T has not been presented before. The results in this article not only can be applied on ordinary differential equations when T = R, difference equations when T = N 0 , but also, can be applied for q-difference equations when T = q N 0 , where q N 0 := {q t : t ∈ N 0 for q > 1} or T = q Z := q Z ∪ {0} for q >1 (which has important applications in quantum theory) and on different types of time scales like T = hN 0 , T = N 2 0 and T = T n the space of the harmonic numbers. Finally, we give some applications to illustrate our main results.

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This paper deals with multiobjective nonlinear programming problems (MONLP). The purpose of this paper is to present an effective approach for solving (MONLP), which is very effective in finding many local pareto-optimal solution,-and the method presented here seems to be very efficient for finding the global efficient solution in the case of a bounded feasible region. We apply the technique of differential equation approach, where the (MONLP) is transformed to a nonlinear autonomous system of differential equations, and the relation between the critical points of differential system and local pareto~optimal solutions of the original optimization problem is proved. Finally, the approach presented in this paper is demonstrated with a numerical simple example.

A new method for obtaining sensitivity information for parametric vector optimization problems (VOP)v is presented, where the parameters in the objective functions and anywhere in the constraints. This method depends on using differential equations technique for solving multiobjective nonlinear programing problems which is very effective in finding many local Pareto optimal solutions. The behavior of the local solutions for slight perturbation of the parameters in the neighborhood of their chosen initial values is presented by using the technique of trajectory continuation. Finally some examples are given to show the efficiency of the proposed method