Existence and uniqueness of positive and nondecreasing solutions for a class of fractional boundary value problems involving the p-Laplacian operator


Araci S., ŞEN E., AÇIKGÖZ M., Srivastava H. M.

ADVANCES IN DIFFERENCE EQUATIONS, 2015 (SCI İndekslerine Giren Dergi) identifier identifier

Özet

In this article, we investigate the existence of a solution arising from the following fractional q-difference boundary value problem by using the p-Laplacian operator: D-q(gamma)(phi(p)(D(q)(delta)y(t))) + f(t,y(t)) = 0 (0 < t < 1; 0 < gamma < 1; 3 < delta < 4), y(0) = (D(q)y)(0) = (D(q)(2)y)(0) = 0, a(1)(D(q)y)(1) + a(2)(D(q)(2)y)(1) = 0, a(1) + vertical bar a(2)vertical bar not equal 0, D(0+)(gamma)y(t)vertical bar(t=0) = 0. We make use of such a fractional q- difference boundary value problem in order to show the existence and uniqueness of positive and nondecreasing solutions by means of a familiar fixed point theorem.