Fractional Multi-point Boundary Value Problems Research Articles

Solvability for a Higher Order Implicit Fractional Multi-point Boundary Value Problems at Resonance

Solvability for a Higher Order Implicit Fractional Multi-point Boundary Value Problems at Resonance

A study of the multipoint boundary value problem for nonlinear differential equations of arbitrary fractional order based on the fixed point theorem for composite nonlinear operators

Abstract The existence and distinctiveness of solutions, as well as the iterative approximations of the distinctive answer to the initial boundary value issue of nonlinear differential equations, may be solved with the help of the theory of nonlinear operators, which offers a strong theoretical guarantee and a fundamental tool. In this work, we examine the fixed point theory for composites nonlinear operators, which may offer a fresh approach to solving linear differential equations having arbitrary order fractional multipoint boundary value problems. The existing result of the boundary value issue’s solution is confirmed by the fixed point theorem for composites nonlinear operators, and the four-point boundary value problem for fractional-order linear equations of the Riemann-Liouville type is examined. A group of fractional-order nonlinear differential equations with deviating quantities are examined to examine the presence of an unusual positive solution for this boundary value problem. The existence of this unique positive solution is determined by the use of both the mixed monotone operator and the combined nonlinear operator fixed point theorem. Ultimately, the nonlinear Bagley-Torvik equation with a fractional order variable coefficient four-point boundary value problem is converted into a Fredholm-Hammerstein integral the formula of the second type with weakly singular or continuous kernels, and the fixed point principle is used to demonstrate the uniqueness of the solution in the space of continuous functions. Approximate solutions are provided for the second class of nonlinear Fredholm-Hammerstein integral equations with weakly singular kernels. The outcomes demonstrate the applicability and validity of the fixed point theorem to composite nonlinear operators, offering a fresh approach to solving the multipoint boundary value issue for nonlinear differential equations of any fractional order.

Multipoint boundary value problem for a coupled system of psi-Hilfer nonlinear implicit fractional differential equation

This study examines the existence and uniqueness of the solution to the coupled system of the ψ-Hilfer nonlinear implicit fractional multipoint boundary value problem. The uniqueness is shown by the Banach contraction principle, and the existence is shown by Krasnosel’skii’s fixed point theorem in a special working space. An example is presented to verify our results. The existence and uniqueness of the solution are analysed graphically.

Lyapunov-type inequalities for fractional multi-point boundary value problems using a new generalized fractional derivative

Lyapunov-type inequalities for fractional multi-point boundary value problems using a new generalized fractional derivative

A shooting like method based on the shifted Chebyshev polynomials for solving nonlinear fractional multi-point boundary value problem

An iterative shooting-like method based on the shifted Chebyshev polynomials is proposed for solving the nonlinear fractional boundary value problems with the multi-point boundary conditions. The proposed method can be applied easily to various nonlocal linear boundary conditions. Here, we investigate the convergence of the proposed method for the nonlinear problems with the multi-point boundary condition. We investigate the convergence of the proposed method for the nonlinear problems with the multi-point boundary conditions. The obtained numerical results confirm the theoretical results and show the efficiency and accuracy of the proposed method.

Solvability for a system of Hadamard fractional multi-point boundary value problems

In this paper, we study a system of Hadamard fractional multi-point boundary value problems. We first obtain triple positive solutions when the nonlinearities satisfy some bounded conditions. Next, we also obtain a nontrivial solution when the nonlinearities can be asymptotically linear growth. Furthermore, we provide two examples to illustrate our main results.

Existence of an approximate solution for a class of fractional multi-point boundary value problems with the derivative term

In this paper, we consider a class of fractional boundary value problems with the derivative term and nonlinear operator term. By establishing new mixed monotone fixed point theorems, we prove these problems to have a unique solution, and we construct the corresponding iterative sequences to approximate the unique solution.

New Lyapunov-type inequalities for fractional multi-point boundary value problems involving Hilfer-Katugampola fractional derivative

<abstract><p>In this paper, we present new Lyapunov-type inequalities for Hilfer-Katugampola fractional differential equations. We first give some unique properties of the Hilfer-Katugampola fractional derivative, and then by using these new properties we convert the multi-point boundary value problems of Hilfer-Katugampola fractional differential equations into the equivalent integral equations with corresponding Green's functions, respectively. Finally, we make use of the Banach's contraction principle to derive the desired results, and give a series of corollaries to show that the current results extend and enrich the previous results in the literature.</p></abstract>

EXISTENCE AND MULTIPLICITY OF POSITIVE SOLUTIONS FOR A SYSTEM OF NONLINEAR FRACTIONAL MULTI-POINT BOUNDARY VALUE PROBLEMS WITH <i>P</i> -LAPLACIAN OPERATOR

<abstract> In this paper, we deal with a coupled system of nonlinear fractional multi-point boundary value problems with $ p $-Laplacian operator. The existence and multiplicity of positive solutions are obtained by employing Leray-Schauder alternative theory, Leggett-Williams fixed point theorem and Avery-Henderson fixed point theorem. As an application, two examples are given to illustrate the effectiveness of our main results. </abstract>

Fractional multipoint boundary value problems at resonance with kernel dimension greater than one

Based on the well‐known coincidence degree theory of Mawhin, we have obtained a new existence result for a class of fractional boundary value problems at resonance when the differential operator has kernel 2. An example of an application supports our result.

Solvability of Fractional Multi-Point Boundary Value Problems with Nonlinear Growth at Resonance

This work is concerned with the solvability of multi-point boundary value problems for fractional differential equations with nonlinear growth at the resonance. Existence results are obtained with the use of the coincidence degree theory. As an application, we discuss an example to illustrate the obtained results.

Existence of Solutions for Fractional Multi-Point Boundary Value Problems on an Infinite Interval at Resonance

This paper aims to investigate a class of fractional multi-point boundary value problems at resonance on an infinite interval. New existence results are obtained for the given problem using Mawhin’s coincidence degree theory. Moreover, two examples are given to illustrate the main results.

Existence results for a coupled system of nonlinear fractional multi-point boundary value problems at resonance

By using the coincidence degree theory, we present an existence result for a coupled system of nonlinear fractional differential equations with multi-point boundary conditions at resonance.

Existence of solutions for fractional multi-point boundary value problems at resonance with three-dimensional kernels

In this paper, by using Mawhin’s continuation theorem, we investigate the existence of solutions for a class of fractional differential equations with multi-point boundary value problems at resonance, and the dimension of the kernel for a fractional differential operator is three. An example is given to show our main result.

Positive Solutions for Singular Semipositone Fractional Differential Equation Subject to Multipoint Boundary Conditions

Existence result together with multiplicity result of positive solutions of higher-order fractional multipoint boundary value problems is given by considering the integrations of height functions on some special bounded sets. The nonlinearity may change its sign and may possess singularities on the time and the space variables at the same time.

Nontrivial Solutions of Higher-Order Nonlinear Singular Fractional Differential Equations with Fractional Multi-point Boundary Conditions

Abstract This paper deals with the existence and multiplicity of nontrivial solutions of fractional multi-point boundary value problems for higher-order nonlinear singular fractional differential equations with sign-changing nonlinear term. The main tool used in the proof is topological degree theory. Some examples are given to illustrate our main results.

Solvability for an impulsive fractional multi-point boundary value problem at resonance

In this paper, we consider the fractional multi-point boundary value problem with impulse effects. As indicated by M Feckan, Y Zhou and JR Wang in 2012, the concepts of piecewise continuous solutions used in most of the current literature about the impulsive differential equations of fractional order are not appropriate. Based on a new concept of a piecewise continuous solution, we establish sufficient conditions for the existence of the solutions for the boundary value problem at resonance by the continuation theorem of coincidence degree theory.

Positive Solutions for Fractional Differential Equations with Multi-Point Boundary Value Problems

In this paper, a fractional multi-point boundary value problem is considered. By using the fixed point index theory and Krein-Rutman theorem, some results on existence are obtained.

The existence of solutions for nonlinear fractional multipoint boundary value problems at resonance

Abstract A class of nonlinear fractional multipoint boundary value problems at resonance is considered in this article. The existence results are obtained by the method of the coincidence degree theory of Mawhin. An example is given to illustrate the results. MSC:34A08.

The Existence of Solutions for a Nonlinear Fractional Multi-Point Boundary Value Problem at Resonance

We discuss the existence of solution for a multipoint boundary value problem of fractional differential equation. An existence result is obtained with the use of the coincidence degree theory.