In the present paper, the analytical solution for an exact second order fuzzy initial value problem under generalized Hukuhara differentiability is obtained. First the solution of first order linear fuzzy differential equation under generalized Hukuhara differentiability is investigated using integration factor methods in two cases. The second based on the type of generalized Hukuhara different...

This work deals with shape optimization of an elastic body in sliding contact (Signorini) a rigid foundation. The mechanical problem is written under its augmented Lagrangian formulation, then solved using classical iterative approach. For practical reasons we are interested applying the process respect to intermediate solution produced by method. Because projection operator involved at each it...

Given an oblique reflection map Γ and functions ψ, χ ∈ Dlim (the space of R -valued functions that have finite left and right limits at every point), the directional derivative ∇χΓ(ψ) of Γ along χ, evaluated at ψ, is defined to be the pointwise limit, as ε ↓ 0, of the family of functions ∇εχΓ(ψ) . = ε [Γ(ψ + εχ) − Γ(ψ)]. Directional derivatives are shown to exist and lie in Dlim for oblique ref...

In this paper, we defined the interval form of \(\alpha, \beta\) level set for triangular q-rung orthopair fuzzy (qROPF) number. To obtain a differentiability notion qROPF valued functions, Hukuhara (H-differentiability) and level-wise H-differentiability is defined. Using KKT optimality condition optimization problem with objective function are formulated.

In this paper, we study the numerical method for solving second-order fuzzy differential equations using Adomian method under strongly generalized differentiability. And, we present an example with initial condition having four different solutions to illustrate the efficiency of the proposed method under strongly generalized differentiability. Keywords—Fuzzy-valued function, Fuzzy initial value...

This talk deals with stability and sensitivity analysis for optimal control problems of an ordinary differential equation with a first-order state constraint. We consider the case when the Hamiltonian and the state constraint are regular. Malanowski (2) obtained Lipschitz continuity and directional differentiability of solutions in L, using generalized implicit functions theorems in infinite di...

The paper concerns parameter dependent nonlinear optimal control problems, subject to state constraints of the first order. In recent papers of the author (see [1, 2, 3, 4]), weakened conditions are derived, under which the solutions and Lagrange multipliers of the problems are locally Lipschitz continuous and directionally differentiable functions of the parameter. The conditions consist of st...

When analyzing point-referenced spatial data, interest will be in the first order or global behavior of associated surfaces. However, in order to better understand these surfaces, we may also be interested in second order or local behavior, e.g., in the rate of change of a spatial surface at a given location in a given direction. In a Bayesian parametric setting, such smoothness analysis has be...