Unique iterative solution for high-order nonlinear fractional q-difference equation based on ψ − ( h , r ) $\psi -(h,r)$ -concave operators

Abstract

Abstract An objective of this paper is to investigate the boundary value problem of a high-order nonlinear fractional q-difference equation. It was to obtain a unique iterative solution for this problem by means of applying a novel fixed-point theorem of ψ − ( h , r ) $\psi -(h,r)$ -concave operator, in which the operator is increasing and defined in ordered sets. Moreover, we construct a monotone explicit iterative scheme to approximate the unique solution. Finally, we give an example to illustrate the use of the main result.

Keywords

• Fractional q-difference equations
• Monotone iterative scheme
• ψ − ( h , r ) $\psi -(h,r)$ -concave operator
• Fixed-point theorem
• Boundary value problem