Integral Boundary Value Problems Research Articles

Positive solutions to integral boundary value problems for singular delay fractional differential equations

<abstract><p>Delay fractional differential equations play very important roles in mathematical modeling of real-life problems in a wide variety of scientific and engineering applications. The objective of this manuscript is to study the existence and uniqueness of positive solutions for singular delay fractional differential equations with integral boundary data. To investigate the described system, we construct a $ u_0 $-positive operator first. New research technique of by constructing $ u_0 $-positive operator is used to overcome the difficulties caused by both the delays and the boundary value conditions. Then the sufficient conditions for the existence and uniqueness of positive solutions of a class of the singular delay fractional differential equations with integral boundary is proved by using the fixed point theorem in cone.</p></abstract>

Positive solutions for integral boundary value problems of nonlinear fractional differential equations with delay

In this study, we consider integral boundary value problems of nonlinear fractional differential equations with finite delay. Existence results of positive solutions for the problems are obtained on the basis of the Guo-Krasnoselskii theorem and the Leggett-Williams fixed point theorem. Comprehensive examples follow the main results in the respective sections.

Existence of solutions for Caputo fractional iterative equations under several boundary value conditions

<abstract><p>In this paper, we investigate the existence and uniqueness of solutions for nonlinear quadratic iterative equations in the sense of the Caputo fractional derivative with different boundary conditions. Under a one-sided-Lipschitz condition on the nonlinear term, the existence and uniqueness of a solution for the boundary value problems of Caputo fractional iterative equations with arbitrary order is demonstrated by applying the Leray-Schauder fixed point theorem and topological degree theory, where the solution for the case of fractional order greater than 1 is monotonic. Then, the existence and uniqueness of a solution for the period and integral boundary value problems of Caputo fractional quadratic iterative equations in $ R^N $ are also demonstrated. Furthermore, the well posedness of the control problem of a nonlinear iteration system with a disturbance is established by applying set-valued theory, and the existence of solutions for a neural network iterative system is guaranteed. As an application, an example is provided at the end.</p></abstract>

On Ψ-Hilfer Fractional Integro-Differential Equations with Non-Instantaneous Impulsive Conditions

We establish sufficient conditions for the existence of solutions of an integral boundary value problem for a Ψ-Hilfer fractional integro-differential equations with non-instantaneous impulsive conditions. The main results are proved with a suitable fixed point theorem. An example is given to interpret the theoretical results. In this way, we generalize recent interesting results.

Positive Solutions for a Class of Integral Boundary Value Problem of Fractional q-Difference Equations

This paper studies a class of integral boundary value problem of fractional q-difference equations. We first give an explicit expression for the associated Green’s function and obtain an important property of the function. The new property allows us to prove sufficient conditions for the existence of positive solutions based on the associated parameter. The results are derived from the application of a fixed point theorem on order intervals.

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.

ON EXISTENCE AND STABILITY RESULTS FOR PANTOGRAPH FRACTIONAL BOUNDARY VALUE PROBLEMS

In this paper, we investigated some essential provisions for the existence and stability of the solution to integral boundary value problems with proportional delay of fractional order Atangana–Baleanu–Caputo (ABC) derivative. By the guidance of fixed point theory, we acquire the deserted results. Moreover, different types of Ullam–Hyers stabilities are investigated for the proposed problem. We also provide an appropriate example for illustrative purposes.

Positive Solutions for a System of Riemann–Liouville Type Fractional-Order Integral Boundary Value Problems

In this paper, we use the fixed-point index to establish positive solutions for a system of Riemann–Liouville type fractional-order integral boundary value problems. Some appropriate concave and convex functions are used to characterize coupling behaviors of our nonlinearities.

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.

Uniqueness Result and Iterative Method for Fourth Order p-Laplacian Integral Boundary Value Problems with Different Nonlinear Terms

Uniqueness Result and Iterative Method for Fourth Order p-Laplacian Integral Boundary Value Problems with Different Nonlinear Terms

Free vibrations of rotating pre-twisted blades including geometrically nonlinear pre-stressed analysis

The steady-state equilibrium deformations (SSEDs) caused by centrifugal force field in rotating blades are not necessarily perturbed disturbances. These deformations can be considered as large amplitude deformations, especially for high values of the rotating speed. Accordingly, in the current study, geometrically nonlinear terms are included in the static analysis under centrifugal forces (SACF) to accurately model the stiffening/softening effects in the vibrations of rotating pre-twisted blades. To this end, by developing a shell model based on first-order shear deformation theory (FSDT), nonlinear and linear integral boundary value problems (IBVPs) governing the SSEDs and vibrations of the blade are obtained, respectively. Multi-mode discretization of these IBVPs is carried out by the spectral Chebyshev technique. The discretization of the nonlinear IBVP results in nonlinear algebraic equations. By solving these equations, nonlinear pre-stressed analysis (NPA) is performed to achieve the SACF. Then, the free vibrations of the rotating pre-twisted blade about the determined equilibrium position is investigated. The numerical results show that the natural frequencies obtained in the presence of the nonlinear terms are extremely lower than those of the linear pre-stressed analysis.

Existence and uniqueness solution for integral boundary value problem of fractional differential equation

In this work, we will study the existence and uniqueness results of a class of nonlinear fractional differential equations with integral boundary value conditions. By using Leray-Schauder nonlinear alternative and the Banach contraction mapping principle. As an application, an example is given to prove our conclusions.

USER-ORIENTED INTELLIGENCE MINING UNDER THE EXISTENCE OF SOLUTIONS TO INTEGRAL BOUNDARY VALUE PROBLEMS FOR FUZZY PARTIAL FRACTIONAL DIFFERENTIAL EQUATIONS

In order to accurately perceive user intention and improve the reliability of user intention information mining, the existence of solution of integral boundary value problem of fuzzy partial fractional differential equation is used to mine the information of user intention. Firstly, the periodic boundary value problem of fractional order fuzzy linear differential equation, periodic boundary value problem of fractional order fuzzy nonlinear differential equation and periodic boundary value problem of fractional order fuzzy coupled differential system are described in this research. The existence of the solution of the integral boundary value problem of the fuzzy partial fractional order differential equation is proved. Then a user-oriented information mining framework and an evaluation model based on the existence of solutions for the integral boundary value problem of fuzzy partial fractional differential equations are constructed. Finally, this research makes a case study and a comprehensive evaluation of user-oriented information mining based on the existence of solutions of integral boundary value problems for fuzzy partial fractional differential equations. The results show that the method based on the existence of the solution of the integral boundary value problem of fuzzy partial fractional order differential equation is feasible and scientific for the information mining of user intention. It is also concluded that this method is suitable for the modelling and solving of intelligence mining with complicated and unclear user intention. The research provides a good guidance for information mining oriented to user intention.

On Global Convergence of Third-Order Chebyshev-Type Method under General Continuity Conditions

There are very few papers that talk about the global convergence of iterative methods with the help of Banach spaces. The main purpose of this paper is to discuss the global convergence of third order iterative method. The convergence analysis of this method is proposed under the assumptions that Fréchet derivative of first order satisfies continuity condition of the Hölder. Finally, we consider some integral equation and boundary value problem (BVP) in order to illustrate the suitability of theoretical results.

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>

Corrigendum to “The existence of solutions for integral boundary value problems with p-Laplacian operator on infinite interval” [Journal of Nonlinear Functional Analysis, Vol. 2021 (2021), Article ID 13

Corrigendum to “The existence of solutions for integral boundary value problems with p-Laplacian operator on infinite interval” [Journal of Nonlinear Functional Analysis, Vol. 2021 (2021), Article ID 13

THE EXISTENCE OF SOLUTIONS OF INTEGRAL BOUNDARY VALUE PROBLEM FOR HILFER FRACTIONAL DIFFERENTIAL EQUATIONS WITH P-LAPLACIAN AT RESONANCE

By using the extension of the continuous theorem of Ge and Ren, the solvability of integral boundary value problems for Hilfer fractional differential equations with p-Laplacian is investigated. In order to get this conclusion, we construct appropriate Banach spaces and define suitable operators. At the end of the article, an example is given to illustrate our main results.

Asymptotic behavior of the solution of the integral boundary value problem for singularly perturbed integro-differential equations

The work is devoted to clarifying asymptotic with respect to a small parameter behavior of the solution of the integral boundary value problem for singularly perturbed linear integro-differential equation. In the work are obtained analytical formula and asymptotic estimates of the solution for the integral boundary value problem. It is established that the solution of the considered boundary value problem at the ends of a given segment has the phenomena of boundary jumps of the same orders. A modified degenerate boundary value problem is constructed, to the solution of which approaches the solution of assumed singularly perturbed integral boundary value problem. The value of the jump of integral terms is found. &nbsp

Existence and uniqueness results for Riemann–Stieltjes integral boundary value problems of nonlinear implicit Hadamard fractional differential equations

In this paper, we study the existence and uniqueness of solutions for Riemann–Stieltjes integral boundary value problems of nonlinear implicit Hadamard fractional differential equations. The investigation of the main results depends on Schauder’s fixed point theorem and Banach’s contraction principle. An illustrative example is given to show the applicability of theoretical results.

Local existence\u2013uniqueness and monotone iterative approximation of positive solutions for p-Laplacian differential equations involving tempered fractional derivatives

In this paper, we are concerned with a kind of tempered fractional differential equation Riemann–Stieltjes integral boundary value problems with p-Laplacian operators. By means of the sum-type mixed monotone operators fixed point theorem based on the cone P_{h}, we obtain not only the local existence with a unique positive solution, but also construct two successively monotone iterative sequences for approximating the unique positive solution. Finally, we present an example to illustrate our main results.