Positive solutions for a high-order semipositone fractional differential equation with integral boundary conditions

In this paper, we consider the existence of positive solutions for a high-order semipositone fractional differential equation with Riemann-Stieltjes integral boundary conditions. By Krasnoselskii-Zabreiko fixed point theorem and some inequalities associated with Green’s function, two new existence theorems are obtained in the case that the nonlinearity f is allowed to grow both superlinearly and sublinearly. Finally, two examples are given to illustrate the main results.     

Existence results of positive solutions to boundary value problem for fractional differential equation

In this paper, we consider the existence, multiplicity, and nonexistence of positive solutions to some class of boundary vale problem for fractional differential equation of high order. Our analysis relies on the fixed point index.      

Existence of positive solution for singular fractional differential equation

In this paper, we establish the existence of a positive solution to a singular boundary value problem of nonlinear fractional differential equation. Our analysis rely on nonlinear alternative of Leray-Schauder type and Krasnoselskii’s fixed point theorem in a cone.     

Existence and uniqueness of solutions for a nonlinear fractional differential equation

In this paper we prove the existence and uniqueness of solutions for a class of the nonlinear fractional differential equation with initial condition and investigate the dependence of the solution on the order of the differential equation and on the initial condition. Then we give an example to demonstrate the main results.     

Existence and uniqueness of positive solutions to nonlinear fractional differential equation with integral boundary conditions

In this paper, we consider the following nonlinear fractional three-point boundary-value problem:

Existence of positive periodic solutions for a functional differential equation with a parameter

In this paper, we study the existence, multiplicity and nonexistence of positive ω$\omega$-periodic solutions for a kind of nonautonomous functional differential equation by employing the fixed point theorem in cones. Some new results are obtained. As an application of our results, we discuss the existence of a positive periodic solution for a class of models of blood cell production with a parameter, which has not been investigated by using previous methods.     

Existence of positive solutions for the singular fractional differential equations

In this paper, we consider the following two-point fractional boundary value problem. We provide sufficient conditions for the existence of multiple positive solutions for the following boundary value problems that the nonlinear terms contain i-order derivative where n?1<α≤n is a real number, n is natural number and n≥2, α?i>1, i∈N and 0≤i≤n?1. ${}^{c}D_{0^{+}}^{\alpha}$ is the standard Caputo derivative. f(t,x ₀,x ₁,…,x _i ) may be singular at t=0.     

Existence of solutions for fractional differential equation with p-Laplacian through variational method

In this paper, a class of fractional differential equation with p-Laplacian operator is studied based on the variational approach. Combining the mountain pass theorem with iterative technique, the existence of at least one nontrivial solution for our equation is obtained. Additionally, we demonstrate the application of our main result through an example.     

Existence of positive solutions of nonlinear fractional differential equations

Existence of positive solutions for the nonlinear fractional differential equation D^su(x)=f(x,u(x)), 0<s<1, has been studied (S. Zhang, J. Math. Anal. Appl. 252 (2000) 804-812), where D^s denotes Riemann-Liouville fractional derivative. In the present work we study existence of positive solutions in case of the nonlinear fractional differential equation:

L(D)u=f(x,u),u(0)=0,0<x<1,     

Existence of three positive solutions for a class of Riemann-Liouville fractional q-difference equation

In this paper, we confirm the existence of three positive solutions for a class of Riemann-Liouville fractional $q$-difference equation which satisfies the boundary conditions. We gain several sufficient conditions for the existence of three positive solutions of this boundary value problem by applying the Leggett-Williams fixed point theorem.     

Unique positive solutions for fractional differential equation boundary value problems

In this work, we consider the uniqueness of positive solutions for fractional differential equation boundary value problems. Our results can not only guarantee the existence of a unique positive solution, but also be applied to construct an iterative scheme for approximating it.     

Existence of solutions for fractional differential equation three-point boundary value problems

In this paper, by using some fixed point theorems, the existence of unique solution and the existence of at least one solution for a fractional differential equation three-point boundary value problems are established. Finally, some illustrative examples are presented to demonstrate the validity of the main results.     

Existence of positive solutions to a boundary value problem for a delayed singular high order fractional differential equation with sign-changing nonlinearity

In this paper, we discuss the existence of positive solutions to the boundary value problem for a high order fractional differential equation with delay and singularities including changing sign nonlinearity. By using the properties of the Green function, Guo-krasnosel"skii fixed point theorem, Leray-Schauder"s nonlinear alternative theorem, some existence results of positive solutions are obtained, respectively.     

Existence of positive solutions for fractional differential systems with multi point boundary conditions

In this paper, we study the existence of positive solutions to the boundary value problem for the fractional differential system $$\left\{\begin{array}{lll} D_{0^+}^\beta \phi_p(D_{0^+}^\alpha u) (t) = f_1 (t, u (t), v (t)),\quad t \in (0, 1),\\ D_{0^+}^\beta \phi_p(D_{0^+}^\alpha v) (t) = f_2 (t, u (t), v(t)), \quad t \in (0, 1),\\ D_{0^+}^\alpha u(0)= D_{0^+}^\alpha u(1)=0,\; u (0) = 0, \quad u (1)-\Sigma_{i=1}^{m-2} a_{1i}\;u(\xi_{1i})=\lambda_1,\\ D_{0^+}^\alpha v(0)= D_{0^+}^\alpha v(1)=0,\; v (0) = 0, \quad v (1)-\Sigma_{i=1}^{m-2} a_{2i}\; v(\xi_{2i})=\lambda_2, \end{array}\right. $$ where ${1<\alpha,\beta\leq 2, 2 <\alpha + \beta\leq 4, D_{0^+}^\alpha}$ is the Riemann–Liouville fractional derivative of order α. By using the Leggett–Williams fixed point theorem in a cone, the existence of three positive solutions for nonlinear singular boundary value problems is obtained.     

Existence of multiple positive periodic solutions for differential equation with state-dependent delays

By utilizing a fixed point theorem in cones, we present some sufficient conditions which guarantee the existence of multiple positive periodic solutions for a class of differential equations with state-dependent delays. Our results extend and improve some previous results.