MULTIPLE POSITIVE SOLUTIONS OF NONLINEAR BOUNDARY VALUE PROBLEM WITH FINITE FRACTIONAL DIFFERENCE

Abstract

In this paper, we consider a discrete fractional nonlinear boundary value problem in which nonlinear term f is involved with the fractional order difference. We transform the fractional boundary value problem into boundary value problem of integer order difference equation. By using a generalization of LeggettWilliams fixed-point theorem due to Avery and Peterson, we provide sufficient conditions for the existence of at least three positive solutions.

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