Positive solutions for three-point nonlinear fractional boundary value problems

In this paper, we give sufficient conditions for the existence or the nonexistence of positive solutions of the nonlinear fractional boundary value problem \begin{gather*} D_{0^{+}}^{\alpha}u+a(t)f(u(t))=0, 0<t<1, 2<\alpha<3,\\ u(0)=u^{\prime}(0)=0, u^{\prime}(1)-\mu u^{\prime}(\eta)=\lambda, \end{gather*} where $D_{0^{+}}^{\alpha}$ is the standard Riemann-Liouville fractional differential operator of order $\alpha$, $\eta\in\left(0,1\right)$, $\mu\in\left[0,\dfrac{1}{\eta^{\alpha-2}}\right)$ are two arbitrary constants and $\lambda\in\left[ 0,\infty\right)$ is a parameter. The proof uses the Guo-Krasnosel'skii fixed point theorem and Schauder's fixed point theorem

Boundary value problems for nonlinear fractional differential equations

Sufficient conditions are given in this paper for the existence of solutions of the boundary value problems for nonlinear fractional differential equationsinvolving Riemman fractional derivatives operator of arbirary order. The results are obtained using Banach contraction principle and Krasnoselskii's fixed point theorem

BOUNDARY VALUE PROBLEM FOR NONLINEAR CAPUTO-HADAMARD FRACTIONAL DIFFERENTIAL EQUATION WITH HADAMARD FRACTIONAL INTEGRAL AND ANTI-PERIODIC CONDITIONS

The aim of this work is to study a class of boundary value problem including a fractional order differential equation involving the Caputo-Hadamard fractional derivative. Suffcient conditions will be presented to guarantee the existence and uniqueness of solution of this fractional boundary value problem. The boundary conditions introduced in this work are of quite general nature and reduce to many special cases by fixing the parameters involved in the conditions

Existence and attractivity results for ψ -Hilfer hybrid fractional differential equations

In this work, we present some results on the existence of attractive solutions of fractional differential equations of the ψ-Hilfer hybrid type. The results on the existence of solutions are a consequence of the Schauder fixed point theorem. Next, we prove that all solutions are uniformly locally attractive

Monotone Iterative and Upper–Lower Solution Techniques for Solving the Nonlinear ψ−Caputo Fractional Boundary Value Problem

The objective of this paper is to study the existence of extremal solutions for nonlinear boundary value problems of fractional differential equations involving the ψ−Caputo derivative CDa+σ;ψϱ(t)=V(t,ϱ(t)) under integral boundary conditions ϱ(a)=λIν;ψϱ(η)+δ. Our main results are obtained by applying the monotone iterative technique combined with the method of upper and lower solutions. Further, we consider three cases for ψ*(t) as t, Caputo, 2t, t, and Katugampola (for ρ=0.5) derivatives and examine the validity of the acquired outcomes with the help of two different particular examples