A one dimensional stochastic differential equation of the form dX = AXdt+ 1 2 (−A) ∂ξ[((−A)X)]dt+ ∂ξdW (t), X(0) = x is considered, where A = 1 2∂ 2 ξ . The equation is equipped with periodic boundary conditions. When α = 0 this equation arises in the Kardar–Parisi–Zhang model. For α 6= 0, this equation conserves two important properties of the Kardar–Parisi–Zhang model: it contains a quadratic...

In this article, we study sufficient conditions for existence and uniqueness of positive solutions to the following coupled system of fractional order differential equations with antiperiodic boundary conditions { cDαu(t)+ f (t,v(t), Dα−1v(t)) = 0, cDβ v(t)+g(t,u(t), Dβ−1u(t)) = 0, 0 < t < 1, u(0) = −u(1),v(0) = −v(1), Du(0) = −Dpu(1), Dv(0) = −Dqv(1), where 1 < α ,β 2,α − p 1,β − q 1 and 0 < p...

Existence and approximation of best proximity points is an interesting topic for which one can see [2, 3, 4, 6, 5] for more information. Another extension of Banach contraction principle was given by Nieto and Rodriguez-Lopez in partially ordered metric spaces [9]. They proved some fixed point theorems in partially ordered sets in order to show the existence and uniqueness for a first-order ord...

In this paper, we prove the existence of solutions for an anti-periodic boundary value problem of nonlinear impulsive fractional differential equations by applying some known fixed point theorems. Some examples are presented to illustrate the main results.

in this paper, the conjugate gradient method coupled with adjoint problem is used in order to solve the inverse heat conduction problem and estimation of the time- dependent heat flux using the temperature distribution at a point in a three layer system with none homogeneous boundary conditions. also, the effect of noisy data on final solution is studied. for solving this problem the general co...