Abstract This work presents the existential and unique results for solution to a kind of high-order fractional nonlinear differential equations involving Caputo derivative. The boundary condition is integral type, which entangles both starting ending points domain. First, exact extracted in terms Green’s function linear equation, then Banach contraction mapping theorem applied prove main result...

Abstract In this paper, we presented a domain decomposition method via exponential splines for solving singularly perturbed two-point boundary value problems with the boundary layer at one end (left or right) point. The method is distinguished by the following fact: The original singularly perturbed two-point boundary value problem is divided into two problems, namely inner and outer region pro...

In this paper, we investigatethe boundary value problem for differential pencils on the half-linewith a turning point. Using a fundamental system of solutions, wegive a asymptotic distribution of eigenvalues.

1. Solution of a two-point boundary value problem. We consider a linear dynamical system ˙ x = Ax, with x(t) ∈ R n. There is an n-dimensional subspace of solutions of this equation, so to single out one of the trajectories we can impose, roughly speaking, n equations. In the most common situation, we specify x(0) = x 0 , in which case the unique solution is x(t) = e tA x 0. This is called an in...

The focus of the present study is the BBM equation which models unidirectional propagation of small amplitude long waves in shallow water and other dispersive media. Interest will be turned to the two-point boundary value problem wherein the wave motion is specified at both ends of a finite stretch of the medium of propagation. The principal new result is an exact theory of convergence of the t...

This paper presents a successive approximation method (SAM) for solving a large class of optimal control problems. The proposed analytical-approximate method, successively solves the Two-Point Boundary Value Problem (TPBVP), obtained from the Pontryagin's Maximum Principle (PMP). The convergence of this method is proved and a control design algorithm with low computational complexity is present...