On discrete sequential fractional boundary value problems

In this paper, we analyze several different types of discrete sequential fractional boundary value problems. Our prototype equation is - Delta(mu 1) Delta(mu 2) Delta(mu 3) y(t) = f (t + mu(1) + mu(2) + mu(3) - 1, y(t+mu(1) + mu(2) + mu(3) - 1)) subject to the conjugate boundary conditions y(0) = 0 = y(b + 2), where f : [1, b + 1](N0) x R -> [0, +infinity) is a continuous function and mu(1), mu(2), mu(3) epsilon (0,1) satisfy 1 < mu(2) + mu(2) + mu(3) < 2 and 1 < mu(1) + mu(2) + mu(3) < 2. We also obtain results for deltanabla discrete fractional boundary value problems. As an application of our analysis, we give conditions under which such problems will admit at least one positive solution. (C) 2011 Elsevier Inc. All rights reserved.