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In this paper, by using the Avery-Peterson fixed point theorem, we establish the existence result of at least three positive solutions of boundary value problem of nonlinear differential equation with Riemann-Liouville’s fractional order derivative. An example illustrating our main result is given. Our results complements and extends previous work in the area of boundary value problems of nonlinear fractional differential equations.

THREE POSITIVE SOLUTIONS FOR BOUNDARY VALUE PROBLEM FOR DIFFERENTIAL EQUATION WITH RIEMANN-LIOUVILLE FRACTIONAL DERIVATIVE