Nonlocal Multi-point Boundary Conditions Research Articles

Non-local fractional boundary value problems with applications to predator-prey models

We study a nonlinear fractional boundary value problem (BVP) subject to non-local multipoint boundary conditions. By introducing an appropriate parametrization technique we reduce the original problem to an equivalent one with already two-point restrictions. Using a notion of Chebyshev nodes and Lagrange polynomials we construct a successive iteration scheme, that converges to the exact solution of the non-local problem for particular values of the unknown parameters, which are calculated numerically.
 For mote information see https://ejde.math.txstate.edu/Volumes/2023/58/abstr.html

On a self-adjoint coupled system of second-order differential inclusions

A self-adjoint coupled system of second-order differential inclusions with nonlocal multi-point boundary conditions is considered. An existence result is established when the set-valued maps have nonconvex values.

A Langevin-Type q-Variant System of Nonlinear Fractional Integro-Difference Equations with Nonlocal Boundary Conditions

We introduce a new class of boundary value problems consisting of a q-variant system of Langevin-type nonlinear coupled fractional integro-difference equations and nonlocal multipoint boundary conditions. We make use of standard fixed-point theorems to derive the existence and uniqueness results for the given problem. Illustrative examples for the obtained results are also presented.

A Self-Adjoint Coupled System of Nonlinear Ordinary Differential Equations with Nonlocal Multi-Point Boundary Conditions on an Arbitrary Domain

The main object of this paper is to investigate the existence of solutions for a self-adjoint coupled system of nonlinear second-order ordinary differential equations equipped with nonlocal multi-point coupled boundary conditions on an arbitrary domain. We apply the Leray–Schauder alternative, the Schauder fixed point theorem and the Banach contraction mapping principle in order to derive the main results, which are then well-illustrated with the aid of several examples. Some potential directions for related further researches are also indicated.

On the existence and uniqueness of solutions for fractional differential equations with nonlocal multi-point boundary conditions

On the existence and uniqueness of solutions for fractional differential equations with nonlocal multi-point boundary conditions

Existence results for Riemann-Liouville fractional integro-differential inclusions with fractional nonlocal integral boundary conditions

We introduce a new class of problems consisting of Riemann-Liouville fractional integro-differential inclusions supplemented with fractional nonlocal multi-point boundary conditions. The existence results for the given problem are derived in the weighted space with the aid of appropriate fixed point theorems for multi-valued maps. Numerical examples are constructed for the illustration of the obtained results.

Boundary value problems for fractional differential inclusions with nonlocal multipoint boundary conditions

We establish sufficient conditions for the existence of solutions of boundary value problems for a fractional differential inclusion with nonlocal multipoint boundary conditions involving the Caputo type derivative with order α∈(1,2]. Both convex- and nonconvex-valued right-hand sides are considered.

Meshless Analysis of Nonlocal Boundary Value Problems in Anisotropic and Inhomogeneous Media

In this work, meshless methods based on a radial basis function (RBF) are applied for the solution of two-dimensional steady-state heat conduction problems with nonlocal multi-point boundary conditions (NMBC). These meshless procedures are based on the multiquadric (MQ) RBF and its modified version (i.e., integrated MQ RBF). The meshless method is extended to the NMBC and compared with the standard collocation method (i.e., Kansa’s method). In extended methods, the interior and the boundary solutions are approximated with a sum of RBF series, while in Kansa’s method, a single series of RBF is considered. Three different sorts of solution domains are considered in which Dirichlet or Neumann boundary conditions are specified on some part of the boundary while the unknown function values of the remaining portion of the boundary are related to a discrete set of interior points. The influences of NMBC on the accuracy and condition number of the system matrix associated with the proposed methods are investigated. The sensitivity of the shape parameter is also analyzed in the proposed methods. The performance of the proposed approaches in terms of accuracy and efficiency is confirmed on the benchmark problems.

On More General Fractional Differential Equations Involving Mixed Generalized Derivatives with Nonlocal Multipoint and Generalized Fractional Integral Boundary Conditions

This paper deals with the existence of solutions for a new boundary value problem involving mixed generalized fractional derivatives of Riemann-Liouville and Caputo supplemented with nonlocal multipoint boundary conditions. The existence results for inclusion case are also discussed. The nonlinear term belongs to a general abstract space, and our results rely on modern theorems of fixed point. Ulam stability is also presented. We provide some examples that well-illustrate our main results.

Fractional Differential Equations Involving Hadamard Fractional Derivatives with Nonlocal Multi-point Boundary Conditions

In this paper, we investigate the existence and uniqueness of solutions for the Hadamard fractional boundary value problems with nonlocal multipoint boundary conditions. By using Leray-Schauder nonlinear alternative, Leray Schauder degree theory, Krasnoselskii fixed point theorem, Schaefer fixed point theorem, Banach fixed point theorem, Nonlinear Contractions, the existence and uniqueness of solutions are obtained. As an application, two examples are given to demonstrate our results.

Existence and uniqueness of solutions for a class of higher-order fractional boundary value problems with the nonlinear term satisfying some inequalities

This paper focuses on a class of hider-order nonlinear fractional boundary value problems. The boundary conditions contain Riemann–Stieltjes integral and nonlocal multipoint boundary conditions. It is worth mentioning that the nonlinear term and the boundary conditions contain fractional derivatives of different orders. Based on the Schauder fixed point theorem, we obtain the existence of solutions under the hypothesis that the nonlinear term satisfies the Carathéodory conditions. We apply the Banach contraction mapping principle to obtain the uniqueness of solutions. Moreover, by using the theory of spectral radius we prove the uniqueness and nonexistence of positive solutions. Finally, we illustrate our main results by some examples.

On some fractional integro-differential inclusions with nonlocal multi-point boundary conditions

On some fractional integro-differential inclusions with nonlocal multi-point boundary conditions

Existence of Solutions for Singular Second-Order Ordinary Differential Equations with Periodic and Deviated Nonlocal Multipoint Boundary Conditions

This paper studies the existence of continuous solutions for a class of nonlinear singular second-order ordinary differential equations subject to one of the following boundary conditions: periodic-deviated multipoint boundary conditions, periodic-integral boundary conditions, and periodic-nonlocal integral conditions in the Riemann-Stieltjes sense. An existence result based on the Schauder fixed point theorem and Leray-Schauder continuation principle is used to obtain at least one continuous solution for the singular second-order ordinary differential problems. Two examples are given to show the application of our results.

An exact solution method for a class of nonlinear loaded difference equations with multipoint boundary conditions

ABSTRACTSolvability criteria are established and closed-form solutions are obtained for a class of general boundary value problems consisting of an nth-order nonlinear loaded difference equation and nonlocal multipoint boundary conditions. The approach is based on the extension and perturbation theory of operators.

Boundary value problems for Hadamard fractional differential equations with nonlocal multi-point boundary conditions

Boundary value problems for Hadamard fractional differential equations with nonlocal multi-point boundary conditions

On existence of solutions for fractional differential equations with nonlocal multi-point boundary conditions

This paper investigates the existence of solutions for a boundary value problem of nonlinear fractional differential equations with nonlocal boundary conditions. We use Banach fixed point theorem to prove an existence and uniqueness result. Then, by using O’Regan fixed point theorem, we prove an existence result. Finally, illustrative examples of our main results are presented.

Nullity of the second order discrete problem with nonlocal multipoint boundary conditions

In this paper, we investigate several second order discrete problems with non-local multipoint boundary conditions and present obtained results about their nullity.
 The research was partially supported by the Research Council of Lithuania (grant No. MIP-047/ 2014).