This paper is concerned with weak solution of a mixed boundary value problem for the biharmonic equation in the plane. Using Green’s formula, the problem is converted into a system of Fredholm integral equations for the unknown data on different part of the boundary. Existence and uniqueness of the solutions of the system of boundary integral equations are established in appropriate Sobolev spa...

and Applied Analysis 3 In BVP 1.4 – 1.6 , it can be found that the boundary condition 1.5 is dependent on all the x a , x b , x′ a , and x′ b terms. First, existence and uniqueness of solutions of BVP 1.4 – 1.6 is established by combining the method of upper and lower solutions with LeraySchauder degree theory. Then, the general quasilinearization method is applied to construct the approximatio...

in this paper, boundary value problems of fractional order are converted into an optimal control problems. then an approximate solution is constructed from translations and dilations of a b-spline function such that the exact boundary conditions are satisfied. the fractional differential operators are taken in the riemann-liouville and caputo sense. several example are given and the optimal err...

‎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

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.

in this paper a method is presented in details to solve a nonlinear partial differential equation which has many applications in engineering fields. the boundary condition is mixed to be able to define the value of function on its variation on the boundary. examples are given to demonstrate the accuracy and efficiency of the method.