EXISTENCE OF POSITIVE SOLUTIONS OF FRACTIONAL BOUNDARY VALUE PROBLEMS INVOLVING BOUNDED LINEAR OPERATORS

This paper is concerned with boundary value problems for nonlinear fractional differential equations with a nonlinear term involving a bounded linear operator and satisfying boundary conditions containing a bounded linear functional. The explicit expression for an equivalent integral operator for the BVP is given. A recent fixed point theorem is used to obtain the existence of at least three positive solutions. The paper also provides an example as an application of the existence theorem.