The Existence of Positive Solutions for Boundary Value Problem of Nonlinear Fractional Differential Equations

الملخص EN

We consider the existence of positive solutions for the nonlinear fractional differential equations boundary value problem - D 0 + α u ( t ) = f ( t , u ( t ) ) , 0 < t < 1 , u ( 0 ) = u ' ( 0 ) = u ' ( 1 ) = 0 , where 2 < α ≤ 3 is a real number, D 0 + α is the Riemann-Liouville fractional derivative of order α , and f is a given continuous function.

Our analysis relies on the fixed point index theory in cones.