NEW FIXED POINT THEOREMS FOR SUM OPERATORS IN THE SET Ph,e AND THEIR APPLICATIONS TO NONLINEAR FRACTIONAL DIFFERENTIAL PROBLEMS

The paper presents several new fixed point theorems for some sum operators. Without any compactness or continuity assumptions, we establish sufficient conditions for some operators to have unique fixed points and describe sequences converging to the fixed points. The main results are obtained by the cone theory and monotone iterative technique. Besides, as applications, these new fixed point theorems are used to study the existence and uniqueness of solutions for a class of nonlinear fractional differential equations.