Positive solutions of higher order fractional integral boundary value problem with a parameter

In this paper, we study a higher-order fractional differential equation with integral boundary conditions and a parameter. Under different conditions of nonlinearity, existence and nonexistence results for positive solutions are derived in terms of different intervals of parameter. Our approach relies on the Guo–Krasnoselskii fixed point theorem on cones

On a Hadamard-type fractional turbulent flow model with deviating arguments in a porous medium

In this paper, we concern a Hadamard-type fractional-order turbulent flow model with deviating arguments. By using some standard fixed point theorems, the uniqueness, existence and nonexistence of solutions of the fractional turbulent flow model are investigated. Our results are new and are well illustrated with the aid of three examples

Existence of solutions for fractional differential equations with three-point boundary conditions at resonance in Rn\mathbb{R}^n

In this paper, by applying the coincidence degree theory which was first introduced by Mawhin, we obtain an existence result for the fractional three-point boundary value problems in $\mathbb{R}^n$, where the dimension of the kernel of fractional differential operator with the boundary conditions can take any value in $\{1,2,\ldots,n\}$. This is our novelty. Several examples are presented to illustrate the result

Uniqueness of iterative positive solutions for the singular infinite-point p-Laplacian fractional differential system via sequential technique

By sequential techniques and mixed monotone operator, the uniqueness of positive solution for singular p-Laplacian fractional differential system with infinite-point boundary conditions is obtained. Green's function is derived, and some useful properties of Green' function are obtained. Based on these new properties, the existence of unique positive solutions is established, moreover, an iterative sequence and a convergence rate are given, which are important for practical application, and an example is given to demonstrate the validity of our main results

Existence and Multiple Positive Solutions for Boundary Value Problem of Fractional Differential Equation with p

This paper investigates the existence, multiplicity, nonexistence, and uniqueness of positive solutions to a kind of two-point boundary value problem for nonlinear fractional differential equations with p-Laplacian operator. By using fixed point techniques combining with partially ordered structure of Banach space, we establish some criteria for existence and uniqueness of positive solution of fractional differential equations with p-Laplacian operator in terms of different value of parameter. In particular, the dependence of positive solution on the parameter was obtained. Finally, several illustrative examples are given to support the obtained new results. The study of illustrative examples shows that the obtained results are applicable

Existence of positive solutions for a class of nonlinear fractional differential equations with integral boundary conditions and a parameter

In this paper, we study the existence of positive solutions for the following nonlinear fractional differential equations with integral boundary conditions: D0α+u(t) +h(t)f(t,u(t)) = 0, 0<t<1, u(0) = u′(0) = u″(0) = 0, u(1) = λ∫0ηu(s)ds, where 3 < α ≤ 4,0 < η ≤ 1, 0 -< ληαα <1, D0+α is the standard Riemann–Liouville derivative. h(t) is allowed to be singular at t=0 and t=1. By using the properties of the Green function, u0-bounded function and the fixed point index theory under some conditions concerning the first eigenvalue with respect to the relevant linear operator, we obtain some existence results of positive solution