Explicit iteration and unbounded solutions for fractional q–difference equations with boundary conditions on an infinite interval

Abstract

Abstract In this work, a proposed system of fractional boundary value problems is investigated concerning its unbounded solutions’ existence for a class of nonlinear fractional q-difference equations in the context of the Riemann–Liouville fractional q-derivative on an infinite interval. The system’s solution is formulated with the help of Green’s function. A compactness criterion is established in a special space. All the obtained results of uniqueness and existence are investigated with the help of fixed-point theorems. Some essential examples are illustrated to support our main outcomes.

Keywords

• Fractional q-difference equation
• Fractional q-derivative
• Unbounded solution
• Explicit iteration
• Infinite interval