Multiple Positive Solutions of Nonlinear Boundary Value Problem for Finite Fractional Difference

الملخص EN

We consider a discrete fractional nonlinear boundary value problem in which nonlinear term f is involved with the fractional order difference.

And we transform the fractional boundary value problem into boundary value problem of integer order difference equation.

By using a generalization of Leggett-Williams fixed-point theorem due to Avery and Peterson, we provide sufficient conditions for the existence of at least three positive solutions.