Existence of positive solutions for a class of fractional differential equations with the derivative term via a new fixed point theorem

Abstract

Abstract In this paper, we firstly establish the existence and uniqueness of solutions of the operator equation A ( x , x ) + B ( x , x ) + C ( x ) + e = x $A(x,x)+ B(x,x)+C(x)+e = x$ , where A and B are two mixed monotone operators, C is a decreasing operator, and e ∈ P $e\in P$ with θ ≤ e ≤ h $\theta \leq e \leq h$ . Then, using our abstract theorem, we prove a class of fractional boundary value problems with the derivative term to have a unique solution and construct the corresponding iterative sequences to approximate the unique solution.

Keywords

• Existence and uniqueness
• Mixed monotone operator
• Decreasing operator
• Derivative term
• Fractional equation