Multi-point Boundary Value Conditions Research Articles

Multipoint boundary value problems for higher-order Hadamard fractional neutral differential equations and inclusions

In this paper, we consider fractional neutral differential equations with multipoint boundary value conditions involving Hadamard derivatives and integrals. We obtain the existence and uniqueness of the solution of the equation by using several fixed point theorems, and we also consider the Ulam–Hyers stability of the solution. In addition, we study the differential inclusion problem with multipoint boundary value conditions and prove the existence of the solution of the boundary value problem when the multivalued map has convex values. We also give several examples to illustrate the feasibility of the results.

Unified Approach to the Existence of Solutions for a Coupled System of Fractional Differential-Integral Equations with Infinite Points and Riemann–Stieltjes Integral Boundary Conditions

In this article, by using the Schauder fixed point theorem, we first study the existence of solutions for a new coupled system of Caputo fractional differential equations with multipoint boundary value conditions under the assumption that the nonlinear term satisfies two types of the Carathéodory conditions. Using this result, we provide the existence of solutions of the system with infinite points and Riemann–Stieltjes integral boundary conditions, respectively, instead of doing it directly. Finally, we give three examples to illustrate the feasibility of main results.

On a $k$-dimensional system of hybrid fractional differential equations with multi-point boundary conditions

The Sturm-Liouville fraction equations have considerable role applications in some different phenomena such as mechanical and electrical engineering, medicine and physics. Thus, it is better we review different versions of this equation. We study a $k$-dimensional system of Sturm-Liouville hybrid equations y using the $\alpha$-admissible method. We investigate the existence of solutions for the $k$-dimensional system of hybrid equations with some multi-point boundary value conditions. We provide an example to illustrate our main result.

On a fractional hybrid version of the Sturm\u2013Liouville equation

It is well known that the Sturm–Liouville equation has many applications in different areas of science. Thus, it is important to review different versions of the well-known equation. The technique of α-admissible α-ψ-contractions was introduced by Samet et al. in (Nonlinear Anal. 75:2154–2165, 2012). Our aim in this work is to study a fractional hybrid version of the Sturm–Liouville equation by mixing the technique of Samet. In fact, by using the technique of α-admissible α-ψ-contractions, we investigate the existence of solutions for the fractional hybrid Sturm–Liouville equation by using the multi-point boundary value conditions. Also, we review the existence of solutions for a fractional hybrid version of the problem under the integral boundary value conditions. Finally, we provide two examples to illustrate our main results.

Existence of Positive Solution for Fractional Differential Systems with Multipoint Boundary Value Conditions

In this paper, we apply the fixed-point theorems of γ concave and −γ convex operators to establish the existence of positive solutions for fractional differential systems with multipoint boundary conditions. Two examples are given to support our results.

Positive solutions for a class of two-term fractional differential equations with multipoint boundary value conditions

In this article, we study the existence of positive solutions to a class of two-term fractional nonlocal boundary value problems. The existence and multiplicity of positive solutions are established by means of fixed point index theory. The nonlinearity f(t,x) permits a singularity at t = 0,1 and x=0.

A Compact Difference Scheme for Multi-point Boundary Value Problems of Heat Equations

In this paper, a compact difference scheme is established for the heat equations with multi-point boundary value conditions. The truncation error of the difference scheme is $$O(\tau ^2+h^4),$$ where $$\tau$$ and h are the temporal step size and the spatial step size. A prior estimate of the difference solution in a weighted norm is obtained. The unique solvability, stability and convergence of the difference scheme are proved by the energy method. The theoretical statements for the solution of the difference scheme are supported by numerical examples.

Triple positive solutions for semipositone fractional differential equations m-point boundary value problems with singularities and p–q-order derivatives

In this paper, by means of Leggett–Williams and Guo–Krasnosel'skii fixed point theorems, together with height functions of the nonlinearity on different bounded sets, triple positive solutions are obtained for some fractional differential equations with p–q-order derivatives involved in multi-point boundary value conditions. The nonlinearity may not only take negative infinity but also may permit singularities on both the time and the space variables.

Successively iterative method for a class of high-order fractional differential equations with multi-point boundary value conditions on half-line

In this paper, we study the existence of the positive solutions for a class of high-order differential equations with multi-point boundary value conditions involving the Caputo fractional derivative on infinite interval. Moreover, we develop two computable explicit monotone iterative sequences for approximating the two minimal and maximal positive solutions. An example is given to show the applicability of our main results.

Existence Results for a Coupled System of Nonlinear Fractional Boundary Value Problems at Resonance

Some new Banach spaces are established. Based on those new Banach spaces and by using the coincidence degree theory, we present the existence results for a coupled system of nonlinear fractional differential equations with multipoint boundary value conditions at resonance case.

Multiple Positive Solutions to Multipoint Boundary Value Problem for a System of Second-Order Nonlinear Semipositone Differential Equations on Time Scales

We study a system of second-order dynamic equations on time scales(p1u1∇)Δ(t)-q1(t)u1(t)+λf1(t,u1(t),u2(t))=0,t∈(t1,tn),(p2u2∇)Δ(t)-q2(t)u2(t)+λf2(t,u1(t),u2(t))=0, satisfying four kinds of different multipoint boundary value conditions,fiis continuous and semipositone. We derive an interval ofλsuch that anyλlying in this interval, the semipositone coupled boundary value problem has multiple positive solutions. The arguments are based upon fixed-point theorems in a cone.

Existence of Positive Solutions for Multi-Point Boundary Value Problems on Infinite Intervals in Banach Spaces

We investigate the positive solutions of a class of second-order nonlinear singular differential equations with multi-point boundary value conditions on an infinite interval in Banach spaces. The tools we used are the cone theory and Mönch fixed point theorem and a monotone iterative technique. An example is also given to demonstrate the applications of our results, which include and extend some existing results.

Positive Solutions of m-Point Boundary Value Problems for Fractional Differential Equations

We discuss the existence of minimal and maximal positive solutions for fractional differential equations with multipoint boundary value conditions, and new results are given. An example is also given to illustrate the abstract results.

Positive Solutions of Singular Multipoint Boundary Value Problems for Systems of Nonlinear Second-Order Differential Equations on Infinite Intervals in Banach Spaces

The cone theory together with Monch fixed point theorem and a monotone iterative technique is used to investigate the positive solutions for some boundary problems for systems of nonlinear second-order differential equations with multipoint boundary value conditions on infinite intervals in Banach spaces. The conditions for the existence of positive solutions are established. In addition, an explicit iterative approximation of the solution for the boundary value problem is also derived.

Existence of positive solutions for multi-point boundary value problems on infinite intervals in Banach spaces

In this paper, the cone theory and Mönch fixed point theorem combined with a monotone iterative technique are used to investigate the positive solutions of a class of boundary problems for second-order nonlinear singular differential equations with multi-point boundary value conditions on an infinite interval in Banach spaces. The conditions for the existence of a positive solution are established. In addition, an explicit iterative approximation of the solution for the boundary value problem is also derived.

Existence of symmetric solutions for a fourth-order multi-point boundary value problem with a p-Laplacian at resonance

In this paper, we study the existence of nonconstant symmetric solutions for a kind of p-Laplacian fourth-order differential equations with multi-point boundary value conditions. After translating the fourth-order nonlinear equation into a second-order system, we obtain the conditions for solvability of the given boundary value problem. An example is given to illustrate the result.

First order difference equations with maxima and nonlinear functional boundary value conditions

This paper is devoted to the existence of solutions for a problem of first order difference equations with maxima and with nonlinear functional boundary value conditions. Such boundary conditions include, among others, initial, periodic, antiperiodic and multipoint boundary value conditions, as particular cases.