Existence of the positive solutions for a tripled system of fractional differential equations via integral boundary conditions

Abstract

The purpose of this paper, is studying the existence and nonexistence of positive solutions to a class of a following tripled system of fractional differential equations. D^αu(ζ) + a(ζ)f(ζ, v(ζ), ω(ζ)) = 0, u(0) = 0, u(1) = \int_0^1φ(ζ)u(ζ)dζ, D^βv(ζ) + b(ζ)g(ζ, u(ζ), ω(ζ)) = 0, v(0) = 0, v(1) = \int_0^1ψ(ζ)v(ζ)dζ, D^γω(ζ) + c(ζ)h(ζ, u(ζ), v(ζ)) = 0, ω(0) = 0, ω(1) = \int_0^1η(ζ)ω(ζ)dζ, where 0 ≤ ζ ≤ 1, 1 < α, β, γ ≤ 2, a, b, c ∈ C((0, 1), [0, ∞)), φ, ψ, η ∈ L^1[0, 1] are nonnegative and f, g, h ∈ C([0, 1] × [0, ∞) × [0, ∞), [0, ∞)) and D is the standard Riemann-Liouville fractional derivative. Also, we provide some examples to demonstrate the validity of our results.

Keywords

• tripled system
• integral boundary conditions
• existence and nonexistence of positive solutions
• fractional differential equation