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 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Publication Date: 2015
  • Doi Number: 10.1186/s13662-015-0375-0
  • Title of Journal : ADVANCES IN DIFFERENCE EQUATIONS

Abstract

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.