Fractional Integral Boundary Value Problems Research Articles

Positive solutions for a Hadamard-type fractional p-Laplacian integral boundary value problem

In this paper we study the existence of positive solutions to a Hadamard-type fractional integral boundary value problem using fixed point index. We construct a new linear operator and obtain our main results under some conditions concerning the spectral radius of this linear operator. Our method improves and generalizes some results in the literature.

Nontrivial solutions for a Hadamard fractional integral boundary value problem

<abstract><p>In this paper, we studied a Hadamard-type fractional Riemann-Stieltjes integral boundary value problem. The existence of nontrivial solutions was obtained by using the fixed-point method when the nonlinearities can be superlinear, suberlinear, and have asymptotic linear growth. Our results improved and generalized some results of the existing literature.</p></abstract>

Positive solutions for a Riemann-Liouville-type impulsive fractional integral boundary value problem

<abstract><p>In this work, we investigate a Riemann-Liouville-type impulsive fractional integral boundary value problem. Using the fixed point index, we obtain two existence theorems on positive solutions under some conditions concerning the spectral radius of the relevant linear operator. Our method improves and generalizes some results in the literature.</p></abstract>

Solvability for a Hadamard-type fractional integral boundary value problem

In this paper, we study an integral boundary value problem involving a Hadamard-type fractional differential equation. Using fixed point theory and upper-lower solutions, we present some sufficient conditions to obtain existence theorems of positive solutions for the problem. Examples are provided to illustrate our results.

$\alpha$-$(h,e)$-convex operators and applications for Riemann-Liouville fractional differential equations

In this paper, we consider a class of $\alpha$-$(h,e)$-convex operators defined in set $P_{h,e}$ and applications with $\alpha> 1$. Without assuming the operator to be completely continuous or compact, by employing cone theory and monotone iterative technique, we not only obtain the existence and uniqueness of fixed point of $\alpha$-$(h,e)$-convex operators, but also construct two monotone iterative sequences to approximate the unique fixed point. At last, we investigate the existence-uniqueness of a nontrivial solution for Riemann-Liouville fractional differential equations integral boundary value problems by employing $\alpha$-$(h,e)$-convex operators fixed point theorem.

Positive Solutions for a High-Order Riemann-Liouville Type Fractional Integral Boundary Value Problem Involving Fractional Derivatives

In this paper, under some super- and sub-linear growth conditions, we study the existence of positive solutions for a high-order Riemann–Liouville type fractional integral boundary value problem involving fractional derivatives. Our analysis methods are based on the fixed point index and nonsymmetric property of the Green function. Additionally, we provide some valid examples to illustrate our main results.

Multiple positive solutions for higher-order fractional integral boundary value problems with singularity on space variable

In this article, based on further investigation of the properties of the Green function, together with a fixed point theorem due to Avery-Peterson, height functions on special bounded sets are constructed to obtain the existence of triple positive solutions for higher-order fractional integral boundary value problems. The nonlinearity permits singularities both on the time and the space variables.

Ulam-Hyers-Rassias stability for a class of nonlinear implicit Hadamard fractional integral boundary value problem with impulses

<abstract><p>This paper considers a class of nonlinear implicit Hadamard fractional differential equations with impulses. By using Banach's contraction mapping principle, we establish some sufficient criteria to ensure the existence and uniqueness of solution. Furthermore, the Ulam-Hyers stability and Ulam-Hyers-Rassias stability of this system are obtained by applying nonlinear functional analysis technique. As applications, an interesting example is provided to illustrate the effectiveness of main results.</p></abstract>

Existence of positive solutions of mixed fractional integral boundary value problem with p(t)-Laplacian operator

In this paper, we investigate a mixed fractional integral boundary value problem with p(t)-Laplacian operator. Firstly, we derive the Green function through the direct computation and obtain the properties of Green function. For $$p(t)\ne $$ constant, under the appropriate conditions of the nonlinear term, we establish the existence result of at least one positive solution of the above problem by means of the Leray–Schauder fixed point theorem. Meanwhile, we also obtain the positive extremal solutions and iterative schemes in view of applying a monotone iterative method. For $$p(t)=$$ constant, by using Guo–Krasnoselskii fixed point theorem, we study the existence of positive solutions of the above problem. These results enrich the ones in the existing literatures. Finally, some examples are included to demonstrate our main results in this paper and we give out an open problem.

Existence of solutions for Erd\xe9lyi\u2013Kober fractional integral boundary value problems with p ( t )-Laplacian operator

This paper aims to consider the solvability for Erdélyi–Kober fractional integral boundary value problems with p ( t )-Laplacian operator at resonance. By employing the coincidence degree method, some new results on the existence of solutions are acquired.

Existence and monotone iteration of unique solution for tempered fractional differential equations Riemann\u2013Stieltjes integral boundary value problems

The primary objective of this research paper is to investigate two kinds of high-order tempered fractional differential equations integral boundary value problems. By means of the mixed monotone operators fixed point theorems with perturbation and the increasing varphi -(h,sigma )-concave operators fixed point theorems, we can not only guarantee the existence-uniqueness of solution, but also construct successively sequences for approximating the unique solution. In addition, we demonstrate the effectiveness of the main result by using two examples.

Multi-scale orthogonal basis method for nonlinear fractional equations with fractional integral boundary value conditions

In this paper, we investigate the multi-scale orthogonal basis method for fractional integral boundary value problems. We apply the Newton iteration method to linearize the nonlinear problems and employees the idea of collocation method to determine the coefficients of multi-scale orthogonal basis, then the approximation solution is obtained. The error estimation and stable analysis are presented in detailed. The final numerical experiments verify that the accuracy of our method.

On nonlocal fractional symmetric Hanh integral boundary value problems for fractional symmetric Hahn integrodifference equation

In this paper, we propose a boundary value problems for fractional symmetric Hahn integrodifference equation. The problem contains two fractional symmetric Hahn difference operators and three fractional symmetric Hahn integral with different numbers of order. The existence and uniqueness result of problem is studied by using the Banach fixed point theorem. The existence of at least one solution is also studied, by using Schauder's fixed point theorem.

The Henstock‐Kurzweil‐Pettis integral and multiorders fractional differential equations with impulses and multipoint fractional integral boundary conditions in Banach spaces

This paper is devoted to the existence of weak solutions for a multipoint fractional integral boundary value problem of an impulsive nonlinear differential equation involving multiorders fractional derivatives and deviating argument. We make use of an appropriate fixed point theorem combined with the technique of measures of weak noncompactness. Our investigation is considered in a Banach space. The applicability of the obtained results is illustrated by an example.

Existence and iteration of positive solution for fractional integral boundary value problems with p-Laplacian operator

This paper is concerned with an integral boundary value problem of fractional differential equations with p-Laplacian operator. Sufficient conditions ensuring the existence of extremal solutions for the given problem are obtained. Our results are based on the method of upper and lower solutions and monotone iterative technique.

Positive solutions for semipositone fractional integral boundary value problem on the half-line

We investigate a class of semipositone fractional integral boundary value problem on the half-line. Using the fixed point index theorems in a cone, we obtain the existence result of positive solutions.

Properties of Green\u2019s function and the existence of different types of solutions for nonlinear fractional BVP with a parameter in integral boundary conditions

This paper is concerned with the impact of the parameter on the existence of different types of solutions for a class of nonlinear fractional integral boundary value problems with a parameter that causes the sign of Green’s function associated with the BVP to change. By using the Guo–Krasnoselskii fixed point theorem, the Leray–Schauder nonlinear alternative, and the analytic technique, we give the range of the parameter for the existence of strong positive solutions, strong negative solutions, negative solutions, and sign-changing solutions for the boundary value problem. Some examples are given to illustrate our main results.

Positive Solutions for a System of Fractional Integral Boundary Value Problems Involving Hadamard‐Type Fractional Derivatives

In this paper, we use fixed‐point index to study the existence of positive solutions for a system of Hadamard fractional integral boundary value problems involving nonnegative nonlinearities. By virtue of integral‐type Jensen inequalities, some appropriate concave and convex functions are used to depict the coupling behaviors for our nonlinearities fi(i = 1, 2).

On a three-point fractional integral boundary value problem on the half-line

On a three-point fractional integral boundary value problem on the half-line

Existence of Uniqueness and Nonexistence Results of Positive Solution for Fractional Differential Equations Integral Boundary Value Problems

In this paper, we consider a class of fractional differential equations with conjugate type integral conditions. Both the existence of uniqueness and nonexistence of positive solution are obtained by means of the iterative technique. The interesting point lies in that the assumption on nonlinearity is closely associated with the spectral radius corresponding to the relevant linear operator.