Application of Avery–Peterson fixed point theorem to nonlinear boundary value problem of fractional differential equation with the Caputo’s derivative

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

► We study the positive solutions of differential equation with fractional order.
► The Avery–Peterson fixed point theorem are used in these kind of problems.
► Our results complements previous work in the area of BVP to FDEs.