Existence Results for a New Class of Boundary Value Problems of Nonlinear Fractional Differential Equations

In this article, we study the following fractional boundary value problem D 0 + α c u ( t ) + 2 r D 0 + α − 1 c u ( t ) + r 2 D 0 + α − 2 c u ( t ) = f ( t , u ( t ) ) ,   r > 0 ,   0