We consider the Navier-Stokes equations on thin 3D domains Qε = Ω×(0, ε), supplemented mainly with purely periodic boundary conditions or with periodic boundary conditions in the thin direction and homogeneous Dirichlet conditions on the lateral boundary. We prove global existence and uniqueness of solutions for initial data and forcing terms, which are larger and less regular than in previous ...

In this article, an exact analytical solution for thermal buckling analysis of thin functionallygraded (FG) rectangular plates is presented. Based on the classical plate theory and using the principle ofminimum total potential energy, the stability equations are obtained. Since the material properties in FGmaterials are functions of the coordinates (specially the thickness), the stability equat...

In this article, we develop the distributed order fractional hybrid differential equations (DOFHDEs) with linear perturbations involving the fractional Riemann-Liouville derivative of order $0 < q < 1$ with respect to a nonnegative density function. Furthermore, an existence theorem for the fractional hybrid differential equations of distributed order is proved under the mixed $varphi$-Lipschit...

In this paper, we consider some boundary value problems (BVP) for fractional order partial differential equations ‎(FPDE)‎ with non-local boundary conditions. The solutions of these problems are presented as series solutions analytically via modified Mittag-Leffler functions. These functions have been modified by authors such that their derivatives are invariant with respect to fractional deriv...

In this paper, a collocation method for solving high-order linear partial differential equations (PDEs) with variable coefficients under more general form of conditions is presented. This method is based on the approximation of the truncated double exponential second kind Chebyshev (ESC) series. The definition of the partial derivative is presented and derived as new operational matrices of der...

where D 0 denotes the Riemann Liouville fractional derivative of order q, 1 < q < 2, η > 0, f : [0,∞) × R → R and e : [0,∞) → R are given functions satisfying some conditions. The problem (1.1)–(1.2) happens to be at resonance in the sense that the dimension of the kernel of the linear operator Lx = D 0+x is not less than one under boundary conditions (1.2). It should be noted that in recent ye...

Some new necessary and sufficient conditions for the existence of analytic resolving families operators to linear equation with a distributed Riemann–Liouville derivative in Banach space are established. We study unique solvability natural initial value problem fractional derivatives corresponding inhomogeneous equations. These abstract results applied class boundary problems equations time pol...

I will present some new results concerning explicit high-order finite difference methods applied to hyperbolic systems. In particular I will present some new results that support the addition of appropriate artificial dissipation, even for linear problems. Recently, high-order accurate first derivative finite difference operators are were derived that naturally introduce artificial dissipation....

‎The ‎method ‎of ‎quasilinearization ‎is ‎an ‎effective ‎tool ‎to ‎solve nonlinear ‎equations ‎when ‎some ‎conditions‎ on ‎the ‎nonlinear term ‎of ‎the ‎problem ‎are ‎satisfi‎‎ed. ‎W‎hen ‎the ‎conditions ‎hold, ‎applying ‎this ‎techniqu‎e ‎gives ‎two ‎sequences of ‎coupled ‎linear ‎equations‎ and ‎the ‎solutions ‎of ‎th‎ese ‎linear ‎equations ‎are quadratically ‎convergent ‎to ‎the ‎solution ‎o...