Positive Solutions for Three-Point Boundary Value Problem of Fractional Differential Equation with -Laplacian Operator

Positive Solutions for Three-Point Boundary Value Problem of Fractional Differential Equation with p-Laplacian Operator

We investigate the existence ofmultiple positive solutions for three-point boundary value problemof fractional differential equation with p-Laplacian operator −Dt β (φp(Dt α x))(t) = h(t)f(t, x(t)), t ∈ (0, 1), x(0) = 0,Dt γ x(1) = aDt γ x(ξ),Dt α x(0) = 0, where Dt β ,Dt α ,Dt γ are the standard Riemann-Liouville derivatives with 1 < α ≤ 2, 0 < β ≤ 1, 0 < γ ≤ 1, 0 ≤ α − γ − 1, ξ ∈ (0, 1) and t...

Positive Solutions for Boundary Value Problem of Nonlinear Fractional Differential Equation with p-Laplacian Operator

We consider the existence and multiplicity of concave positive solutions for boundary value problem of nonlinear fractional differential equation with p-Laplacian operatorD 0 φp D α 0 u t f t, u t , D 0 u t 0, 0 < t < 1, u 0 u ′ 1 0, u′′ 0 0, D 0 u t |t 0 0, where 0 < γ < 1, 2 < α < 3, 0 < ρ 1, D 0 denotes the Caputo derivative, and f : 0, 1 × 0, ∞ × R → 0, ∞ is continuous function, φp s |s|p−2...

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.

Triple Positive Solutions for Boundary Value Problem of a Nonlinear Fractional Differential Equation

Triple positive solutions of $m$-point boundary value problem on time scales with $p$-Laplacian

‎In this paper‎, ‎we consider the multipoint boundary value problem for one-dimensional $p$-Laplacian‎ ‎dynamic equation on time scales‎. ‎We prove the existence at least three positive solutions of the boundary‎ ‎value problem by using the Avery and Peterson fixed point theorem‎. ‎The interesting point is that the non-linear term $f$ involves a first-order derivative explicitly‎. ‎Our results ...