Nonlocal Three-point Boundary Research Articles

Nontrivial solutions of fourth order ordinary differential equations with nonlocal three-point boundary conditions

Nontrivial solutions of fourth order ordinary differential equations with nonlocal three-point boundary conditions

On the new fractional hybrid boundary value problems with three-point integral hybrid conditions

We investigate some new class of hybrid type fractional differential equations and inclusions via some nonlocal three-point boundary value conditions. Also, we provide some examples to illustrate our results.

Existence theory for nonlocal boundary value problems involving mixed fractional derivatives

In this paper, we develop the existence theory for a new kind of nonlocal three-point boundary value problems for differential equations and inclusions involving both left Caputo and right Riemann–Liouville fractional derivatives. The Banach and Krasnoselskii fixed point theorems and the Leray–Schauder nonlinear alternative are used to obtain the desired results for the singlevalued problem. The existence of solutions for the multivalued problem concerning the upper semicontinuous and Lipschitz cases is proved by applying nonlinear alternative for Kakutani maps and Covitz and Nadler fixed point theorem. Examples illustrating the main results are also presented.

Sequential fractional differential equations with nonlocal boundary conditions on an arbitrary interval

We discuss the existence and uniqueness of solutions for a nonlocal three-point boundary value problem of sequential fractional differential equations on an arbitrary interval [xi, zeta], xi, zetainmathbb{R}. Our results rely on standard fixed point theorems and are well illustrated with examples. The case for non-homogeneous three-point boundary conditions is also discussed.

On Antiperiodic Nonlocal Three-Point Boundary Value Problems for Nonlinear Fractional Differential Equations

We introduce boundary value conditions involving antiperiodic and nonlocal three-point boundary conditions. We solve a nonlinear fractional differential equation supplemented with those conditions. We obtain some existence results for the given problem by applying some standard tools of fixed point theory. These results are well illustrated with the aid of examples.

A higher-order nonlocal three-point boundary value problem for sequential fractional differential equations

A higher-order nonlocal three-point boundary value problem for sequential fractional differential equations

On Higher-Order Sequential Fractional Differential Inclusions with Nonlocal Three-Point Boundary Conditions

We study a nonlinear three-point boundary value problem of sequential fractional differential inclusions of orderξ+1withn-1<ξ≤n,n≥2. Some new existence results for convex as well as nonconvex multivalued maps are obtained by using standard fixed point theorems. The paper concludes with an example.

On the approximation of the boundary layers for the controllability problem of nonlinear singularly perturbed systems

A new systematic approach to the construction of approximate solutions to a class of nonlinear singularly perturbed feedback control systems using the boundary layer functions especially with regard to the possible occurrence of the boundary layers is proposed. For example, problems with feedback control, such as the steady-states of the thermostats, where the controllers add or remove heat, depending upon the temperature registered in another place of the heated bar, can be interpreted with a second-order ordinary differential equation subject to a nonlocal three-point boundary condition. The O(ϵ) accurate approximation of behavior of these nonlinear systems in terms of the exponentially small boundary layer functions is given. At the end of this paper, we formulate the unsolved controllability problem for nonlinear systems.

On nonlocal three-point boundary value problems of Duffing equation with mixed nonlinear forcing terms

In this paper, we investigate the existence and approximation of the solutions of a nonlinear nonlocal three-point boundary value problem involving the forced Duffing equation with mixed nonlinearities. Our main tool of the study is the generalized quasilinearization method due to Lakshmikantham. Some illustrative examples are also presented. Mathematics Subject Classification (2000): 34B10, 34B15.

Generalized approximations for nonlinear three-point boundary value problems

The generalization of the method of quasilinearization for a class of second-order nonlinear nonlocal three-point boundary value problems of the types - x ″ = f ( t , x , x ′ ) , t ∈ [ 0 , 1 ] , x ( 0 ) = 0 , x ′ ( 1 ) = g ( x ( η ) ) , 0 < η ⩽ 1 is developed. A monotone sequence of solutions of linear problems converging uniformly and rapidly to a solution of the problem is obtained in the C 1 norm.

Approximations and rapid convergence of solutions of nonlinear three point boundary value problems

The method of quasilinearization for second order differential equation - x ″ = f ( t , x , x ′ ) , t ∈ [ 0 , 1 ] , with nonlinear nonlocal three-point boundary conditions x ( 0 ) = 0 , x ′ ( 1 ) = g ( x ( η ) ) , 0 < η ⩽ 1 , is developed. A monotone sequence of solutions converging uniformly and rapidly to a unique solution of the problem is obtained.