Existence of Positive Solution for BVP of Nonlinear Fractional Differential Equation

Abstract EN

We consider the following boundary value problem of nonlinear fractional differential equation: ( C D 0 + α u ) ( t ) = f ( t , u ( t ) ) , t ∈ [ 0,1 ] , u ( 0 ) = 0 , u ′ ( 0 ) + u ′′ ( 0 ) = 0 , u ′ ( 1 ) + u ′′ ( 1 ) = 0 , where α ∈ ( 2,3 ] is a real number, C D 0 + α denotes the standard Caputo fractional derivative, and f : [ 0,1 ] × [ 0 , + ∞ ) → [ 0 , + ∞ ) is continuous.

By using the well-known Guo-Krasnoselskii fixed point theorem, we obtain the existence of at least one positive solution for the above problem.