Positive solutions for boundary value problem of fractional differential equation with p-Laplacian operator

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...

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...

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

Existence solutions for new p-Laplacian fractional boundary value problem with impulsive effects

Fractional differential equations have been of great interest recently. This is because of both the intensive development of the theory of fractional calculus itself and the applications of such constructions in various scientific fields such as physics, mechanics, chemistry, engineering, etc. Differential equations with impulsive effects arising from the real world describe the dyn...