Singular Fractional Differential System Research Articles

Positive Solutions for a Class of Nonlinear Singular Fractional Differential Systems with Riemann–Stieltjes Coupled Integral Boundary Value Conditions

In this paper, sufficient conditions ensuring existence and multiplicity of positive solutions for a class of nonlinear singular fractional differential systems are derived with Riemann–Stieltjes coupled integral boundary value conditions in Banach Spaces. Nonlinear functions f(t,u,v) and g(t,u,v) in the considered systems are allowed to be singular at every variable. The boundary conditions here are coupled forms with Riemann–Stieltjes integrals. In order to overcome the difficulties arising from the singularity, a suitable cone is constructed through the properties of Green’s functions associated with the systems. The main tool used in the present paper is the fixed point theorem on cone. Lastly, an example is offered to show the effectiveness of our obtained new results.

Existence of a solution for a multi singular pointwise defined fractional differential system

In this paper, we will investigate the existence of some solutions for a multi singular fractional differential system with some boundary conditions.

Stability analysis of a nonlinear coupled implicit switched singular fractional differential system with p-Laplacian

This paper deals with existence, uniqueness, and Hyers–Ulam stability of solutions to a nonlinear coupled implicit switched singular fractional differential system involving Laplace operator phi _{p}. The proposed problem consists of two kinds of fractional derivatives, that is, Riemann–Liouville fractional derivative of order β and Caputo fractional derivative of order σ, where m-1<beta , sigma < m, min {2,3,dots }. Prior to proceeding to the main results, the system is converted into an equivalent integral form by the help of Green’s function. Using Schauder’s fixed point theorem and Banach’s contraction principle, the existence and uniqueness of solutions are proved. The main results are demonstrated by an example.

Unique iterative positive solutions for a singular p-Laplacian fractional differential equation system with infinite-point boundary conditions

By using the method of mixed monotone operator, a unique positive solution is obtained for a singular p-Laplacian boundary value system with infinite-point boundary conditions in this paper. Green’s function is derived and some useful properties of the Green’s function are obtained. Based upon these new properties and by using mixed monotone operator, the existence results of the positive solutions for the boundary value problem are established. Moreover, the unique positive solution that we obtained in this paper is dependent on lambda ,mu , and an iterative sequence and convergence rate, which are important for practical application, are given. An example is given to demonstrate the application of our main results.

Positive solutions of semipositone singular fractional differential systems with a parameter and integral boundary conditions

AbstractIn this paper, the existence of positive solutions for systems of semipositone singular fractional differential equations with a parameter and integral boundary conditions is investigated. By using fixed point theorem in cone, sufficient conditions which guarantee the existence of positive solutions are obtained. An example is given to illustrate the results.

Denumerably many positive solutions for a n-dimensional higher-order singular fractional differential system

This paper investigates the existence of denumerably many positive solutions and two infinite families of positive solutions for the n-dimensional higher-order fractional differential system mathbf{D}_{0^{+}}^{alpha}mathbf{x}(t)+lambda mathbf{g}(t)mathbf{f}(t,mathbf{x}(t))=0, 0< t<1. The vector-valued function x is defined by mathbf {x}=[x_{1},x_{2},dots,x_{n}]^{top}, mathbf{g}(t)=operatorname{diag}[g_{1}(t), g_{2}(t), ldots, g_{n}(t)], where g_{i}in L^{p}[0,1] for some pgeq 1, i=1,2,ldots, n, and has infinitely many singularities in [0,frac{1}{2}). Our methods employ the fixed point theorems combined with the partially ordered structure of a Banach space.

SOLVABILITY FOR NONLINEAR SINGULAR FRACTIONAL DIFFERENTIAL SYSTEMS WITH MULTI-ORDERS

In this paper, we consider the existence of positive solutions for a class of nonlinear singular fractional differential systems with multi-orders. Our analysis relies on fixed point theorems on cones. Some sufficient conditions for the existence of at least one or two positive solutions for boundary value problem of nonlinear singular fractional differential systems with multi-orders are established. As an application, an example is presented to illustrate the main results.

Existence of Solutions of Impulsive Anti-periodic Type Boundary Value Problems for Singular Fractional Differential Systems

Results on the existence of solutions to a new class of impulsive singular fractional differential systems with multiple base points are established. The assumptions imposed on the nonlinearities, see (D1) and (D2) in Theorem 3.1, are weaker than known ones, (i.e., (A) in Introduction section). The analysis relies on a well known fixed point theorem. An example is given to illustrate the efficiency of the main theorems.

English

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Existence and uniqueness of positive solutions for singular fractional differential systems with coupled integral boundary conditions

Existence and uniqueness of positive solutions for singular fractional differential systems with coupled integral boundary conditions

Positive solutions of singular fractional order differential system with Riemann-Stieltjes integral boundary condition

In this paper, we study the existence of positive solutions to a class of higher-order nonlinear fractional functional differential system with Riemann-Stieltjes integral boundary conditions. Our method relies upon the upper and lower solutions and the Schauder fixed point theorem. Furthermore, we constructed an iterative scheme to approximate the positive solution. We also give an example to illustrate the main results.

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

Positive solutions for higher-order singular fractional differential system with coupled integral boundary conditions

In this paper, we study the positive solutions of a higher-order singular fractional differential system with coupled integral boundary conditions. The conditions for the existence of at least one positive solution are established together with the estimates of the lower and upper bounds of the solution at any instant of time. Our results are based on the method of upper and lower solutions and the Schauder fixed point theorem. In the end, an example is worked out to illustrate our main results.

Existence of global solutions of impulsive IVPs of singular fractional differential systems on half line

Existence of global solutions of impulsive IVPs of singular fractional differential systems on half line

New results on the existence of solutions of boundary value problems for singular fractional differential systems with impulse effects

Results on the existence of solutions to a new class of impulsive singular fractional differential systems with multiple base points are established. The assumptions imposed on the nonlinearities, see ((C) and (D) in Theorem 3.1), are weaker than known ones, (i.e., (A) in Introduction

Positive solution of singular fractional differential system with nonlocal boundary conditions

Abstract In this paper, we consider the existence of positive solutions for a singular fractional differential system involving a nonlocal boundary condition which is given by a linear functional on C [ 0 , 1 ] with a signed measure. By looking for the upper and lower solutions of the system, the sufficient condition of the existence of positive solutions is established; some further cases are discussed. This is proved in the case of strong singularity and with a signed measure. MSC:34B15, 34B25.

Positive Solutions of a Singular Nonlocal Fractional Order Differential System via Schauder’s Fixed Point Theorem

We establish the existence of positive solutions to a class of singular nonlocal fractional order differential system depending on two parameters. Our methods are based on Schauder’s fixed point theorem.

Positive solutions to singular fractional differential system with coupled boundary conditions

By using the fixed point theory in cone and constructing some available integral operators together with approximating technique, the existence of positive solution for a singular nonlinear semipositone fractional differential system with coupled boundary conditions is established. Two examples are then given to demonstrate the validity of our main results.

Existence Results for a Coupled System of Nonlinear Singular Fractional Differential Equations with Impulse Effects

A boundary value problem for the singular fractional differential system with impulse effects is presented. By applying Schauder's fixed point theorem in a suitably Banach space, we obtain the existence of at least one solution for this problem. Two examples are presented to illustrate the main theorem.

The uniqueness of positive solution for a singular fractional differential system involving derivatives

By using the fixed point theorem of the mixed monotone operator, the uniqueness of positive solution for a singular fractional differential system involving derivatives is established. An example is then given to illuminate the application of the main results.