Positive solutions of nonlinear fractional differential equations with integral boundary value conditions

AbstractIn this paper, we consider the existence of positive solutions for a class of nonlinear boundary-value problem of fractional differential equations with integral boundary conditions. Our analysis relies on known Guo–Krasnoselskii fixed point theorem

Monotone iterative technique for time-space fractional diffusion equations involving delay

This paper considers the initial boundary value problem for the time-space fractional delayed diffusion equation with fractional Laplacian. By using the semigroup theory of operators and the monotone iterative technique, the existence and uniqueness of mild solutions for the abstract time-space evolution equation with delay under some quasimonotone conditions are obtained. Finally, the abstract results are applied to the time-space fractional delayed diffusion equation with fractional Laplacian operator, which improve and generalize the recent results of this issue

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 Nonlinear Impulsive Fractional Differential Equations of Order α

We investigate the existence and uniqueness of solutions to the nonlocal boundary value problem for nonlinear impulsive fractional differential equations of order α∈(2,3]. By using some well-known fixed point theorems, sufficient conditions for the existence of solutions are established. Some examples are presented to illustrate the main results

Some existence results for impulsive nonlinear fractional differential equations with mixed boundary conditions

AbstractThis paper investigates the existence and uniqueness of solutions for an impulsive mixed boundary value problem of nonlinear differential equations of fractional order α∈(1,2]. Our results are based on some standard fixed point theorems. Some examples are presented to illustrate the main results

Existence of multiple positive solutions of a nonlinear arbitrary order boundary value problem with advanced arguments

In this paper, we investigate nonlinear fractional differential equations of arbitrary order with advanced arguments \begin{equation*}\left\{\begin {array}{ll} D^\alpha_{0^+} u(t) +a(t)f(u(\theta(t)))=0,&0<t<1,~n-1<\alpha\le n,\\ u^{(i)}(0)=0,&i=0,1,2,\cdots,n-2,\\ ~[D^\beta_{0^+} u(t)]_{t=1}=0,&1\le \beta\le n-2, \end {array}\right.\end{equation*} where $n>3\,\, (n\in\mathbb{N}),~D^\alpha_{0^+}$ is the standard Riemann-Liouville fractional derivative of order $\alpha,$ $f: [0,\infty)\to [0,\infty),$ $a: [0,1]\to (0,\infty)$ and $\theta: (0,1)\to (0,1]$ are continuous functions. By applying fixed point index theory and Leggett-Williams fixed point theorem, sufficient conditions for the existence of multiple positive solutions to the above boundary value problem are established

Positive solutions of arbitrary order nonlinear fractional differential equations with advanced arguments

In this paper, we investigate the existence and uniqueness of positive solutions to arbitrary order nonlinear fractional differential equations with advanced arguments. By applying some known fixed point theorems, sufficient conditions for the existence and uniqueness of positive solutions are established

Existence results and the monotone iterative technique for systems of nonlinear fractional differential equations

AbstractBy establishing a comparison result and using the monotone iterative technique combined with the method of upper and lower solutions, we investigate the existence of solutions for systems of nonlinear fractional differential equations