Lower and Upper Solutions for General Two-Point Fractional Order Boundary Value Problems

Year 2015, Volume: 5 Issue: 1, 80 - 87, 01.06.2015

K. R. Prasad B. M. B. Krushna

Abstract

This paper establishes the existence of a positive solution of fractional order two-point boundary value problem, D q1 a+ y t + f t, y t = 0, t ∈ [a, b], y a = 0, y ′ a = 0, αDq2 a+ y b − βDq3 a+ y a = 0, where D qi a+ , i = 1, 2, 3 are the standard Riemann-Liouville fractional order derivatives, 2 < q1 ≤ 3, 0 < q2, q3 < q1, α, β are positive real numbers and b > a ≥ 0, by an application of lower and upper solution method and fixed-point theorems

Keywords

Fractional derivative, Boundary value problem, Two-point, Green’s function, Positive solution

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