Positive Solutions of Nonlocal Boundary Value Problem for High-Order Nonlinear Fractional q-Difference Equations. (14th November 2013) - Yu, Changlong; Wang, Jufang
Abstract : We study the nonlinear q -difference equations of fractional order ( D q α u ) ( t ) + f ( t, u ( t ) ) = 0, 0 < t < 1, ( D q i u ) ( 0 ) = 0, ( D q β u ) ( 1 ) = a ( D q β u ) ( η ), 0 ≤ i ≤ n - 2, where D q α is the fractional q -derivative of the Riemann-Liouville type of order α, n - 1 < α ≤ n, α > 2, 1 ≤ β ≤ n - 2, and 0 ≤ a ≤ 1 . We obtain the existence and multiplicity results of positive solutions by using some fixed point theorems. Finally, we give examples to illustrate the results.