Positive Solutions for a High-Order Riemann-Liouville Type Fractional Integral Boundary Value Problem Involving Fractional Derivatives

Extremal solutions for p-Laplacian fractional differential systems involving the Riemann-Liouville integral boundary conditions

where D , D , and D are the standard Riemann-Liouville fractional derivatives, I and I are the Riemann-Liouville fractional integrals, and 0 < γ < 1 < β < 2 < α < 3, ν,ω > 0, 0 < η, ξ < 1, k ∈R, f ∈ C([0, 1]×R×R,R), g ∈ C([0, 1]×R,R). The p-Laplacian operator is defined as φp(t) = |t|p–2t, p > 1, and (φp) = φq, 1 p + 1 q = 1. The study of boundary value problems in the setting of fractional cal...

Multiple Positive Solutions of a Singular Semipositone Integral Boundary Value Problem for Fractional q-Derivatives Equation

and Applied Analysis 3 The q-integral of a function f defined in the interval [0, b] is given by

Multiple positive solutions for nonlinear boundary value problem of fractional order differential equation with the Riemann-Liouville derivative

*Correspondence: [email protected] Department of Mathematics, Hefei Normal University, Hefei, Anhui 230061, China Abstract In this paper, by means of the Avery-Peterson fixed point theorem, we establish the existence result of a multiple positive solution of the boundary value problem for a nonlinear differential equation with Riemann-Liouville fractional order derivative. An example illustrating...

Existence of positive solutions for a boundary value problem of a nonlinear fractional differential equation

This paper presents conditions for the existence and multiplicity of positive solutions for a boundary value problem of a nonlinear fractional differential equation. We show that it has at least one or two positive solutions. The main tool is Krasnosel'skii fixed point theorem on cone and fixed point index theory.

Multiple Positive Solutions for a Fractional Boundary Value Problem with Fractional Integral Deviating Argument