‎in this paper‎, ‎we study the boundary-value problem of fractional‎ ‎order dynamic equations on time scales‎, ‎$$‎ ‎^c{delta}^{alpha}u(t)=f(t,u(t)),;;tin‎ ‎[0,1]_{mathbb{t}^{kappa^{2}}}:=j,;;1

this paper presents time domain fundamental solutions for the extended biot's dynamic formulations of two-dimensional (2d) unsaturated poroelasticity. unsaturated porous media is considered as a porous media in which the voids are saturated with two immiscible fluids, i.e. liquid and gas. at first, the corresponding explicit laplace transform domain fundamental solution is obtained in term...

a class of new methods based on a septic non-polynomial spline function for the numerical solution of problems in calculus of variations is presented. the local truncation errors and the methods of order 2th, 4th, 6th, 8th, 10th, and 12th, are obtained. the inverse of some band matrixes are obtained which are required in proving the convergence analysis of the presented method. convergence anal...

in this work, we study the performance of the sinc-collocation method for solving bratu's problem. for different choices of step size, we consider the maximum absolute errors in the solutions at sinc grid points and tabulated in tables. the comparison of the obtained results veri ed that this method converges to the exact solution rapidly and with

in this article, we verify existence and uniqueness of positive and nondecreasing solution for nonlinear boundary value problem of fractional differential equation in the form d_{0^{+}}^{alpha}x(t)+f(t,x(t))=0, 0x(0)= x'(0)=0, x'(1)=beta x(xi), where $d_{0^{+}}^{alpha}$ denotes the standard riemann-liouville fractional derivative, 0an illustrative example is also presented.

a boundary integral method is used to simulate spilling breakers. the bottom is also included inthe introduced closed boundary and the problem is directly solved in the physical plane. the method has beenshown to be remarkably stable, and no numerical instability has occurred in any of the calculations. theresults reveal that both the momentum and total energy are almost constant in time during...

in this paper, we study the nehari manifold and its application on the following navier boundary valueproblem involving the p-biharmonic          0, on( ) 1 ( , ) , in , 2*2u uf x u u upu u p q where  is a bounded domain in rn with smooth boundary  . we prove that the problem has atleast two nontrivial nonnegtive solutions when the parameter  belongs to a certain subset o...

in this article, we study the new streamline diffusion finite element for treating the linear second order hyperbolic initial-boundary value problem. we prove a posteriori $ l^2(l^2)$ and error estimates for this method under minimal regularity hypothesis. test problem of an application of the wave equation in the laser is presented to verify the efficiency and accuracy of the method.