Fractional Differential Equations

In this paper, uniqueness results for boundary value problem of fractional differential equation are obtained. Both the Banach's contraction mapping principle and the theory of linear operator are used, and a comparison between the obtained results is provided.

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New uniqueness results for boundary value problem of fractional differential equation

On the uniqueness of solutions for a class of fractional differential equations

In this paper, we focus on the convergence analysis and error estimation for the unique solution of a p-Laplacian fractional differential equation with singular decreasing nonlinearity. By introducing a double iterative technique, in the case of the nonlinearity with singularity at time and space variables, the unique positive solution to the problem is established. Then, from the developed iterative technique, the sequences converging uniformly to the unique solution are formulated, and the estimates of the error and the convergence rate are derived.

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The convergence analysis and error estimation for unique solution of a p -Laplacian fractional differential equation with singular decreasing nonlinearity

The existence and nonexistence of entire large solutions for a quasilinear Schrödinger elliptic system by dual approach

In this paper, we investigate the existence of at least three positive solutions to a singular boundary value problem of Caputo's fractional differential equations with a boundary condition involving values at infinite number of points. Firstly, we establish Green's function and its properties. Then, the existence of multiple positive solutions is obtained by Avery–Peterson's fixed point theorem. Finally, an example is given to demonstrate the application of our main results.

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Existence of positive solutions for singular fractional differential equations with infinite-point boundary conditions

By using the method of reducing the order of a derivative, the higher-order fractional differential equation is transformed into the lower-order fractional differential equation and combined with the mixed monotone operator, a unique positive solution is obtained in this paper for a singular p-Laplacian boundary value system with the Riemann–Stieltjes integral boundary conditions. This equation system is very wide because there are many parameters, which can be changeable in the equation system in this paper, and the nonlinearity is allowed to be singular in regard to not only the time variable but also the space variable. Moreover, the unique positive solution that we obtained in this paper is dependent on λ, and an iterative sequence and convergence rate are given, which are important for practical application. An example is given to demonstrate the application of our main results.

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Iterative unique positive solutions for singular p-Laplacian fractional differential equation system with several parameters

In this paper, we consider a class of singular fractional differential equations with infinite-point boundary conditions. The fractional orders are involved in the nonlinearity of the boundary value problem, and the nonlinearity is allowed to be singular with respect to not only the time variable but also to the space variable. Firstly, we give Green’s function and establish its properties. Then, we utilize the sequential technique and regularization to investigate the existence of positive solutions. Finally, we give an example of application of our result.

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Existence of positive solutions for singular higher-order fractional differential equations with infinite-point boundary conditions

The uniqueness of positive solution for a class of singular fractional differential system with integral boundary conditions is considered in this paper and many types of equation system are contained in this equation system because there are many parameters which can be changeable in this equation system. The fractional orders are involved in the nonlinearity of the boundary value problem and the nonlinearity is allowed to be singular in regard to not only time variable but also space variable. The existence of uniqueness of positive solution is mainly obtained by fixed point theorem of mixed monotone operator and the positive solution of equation system is dependent on λ. An iterative sequence and convergence rate are given which are important for practical application and an example is given to demonstrate the validity of our main results.

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Uniqueness of iterative positive solutions for the singular fractional differential equations with integral boundary conditions

The existence of maximal and minimal positive solutions for singular infinite-point p-Laplacian fractional differential equation is investigated in this paper. Green's function is derived, and some properties of Green's function are obtained. Based upon these properties of Green's function, the existence of maximal and minimal positive solutions is obtained, and iterative schemes are established for approximating the maximal and minimal positive solutions.

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Limin Guo

Papers

Existence of positive solutions for singular fractional differential equations with infinite-point boundary conditions

Iterative unique positive solutions for singular p-Laplacian fractional differential equation system with several parameters

Existence of positive solutions for singular higher-order fractional differential equations with infinite-point boundary conditions

Uniqueness of iterative positive solutions for the singular fractional differential equations with integral boundary conditions

Maximal and minimal iterative positive solutions for singular infinite-point p-Laplacian fractional differential equations