Monotone iterative method for nonlinear fractional \(q\)-difference equations with integral boundary conditions. (English) Zbl 1422.39028
Summary: This paper investigates the existence of positive solutions for a class of nonlinear fractional \(q\)-difference equations with integral boundary conditions. By applying monotone iterative method and some inequalities associated with the Green’s function, the existence results of positive solutions and two iterative schemes approximating the solutions are established. An explicit example is given to illustrate the main result.
MSC:
| 39A13 | Difference equations, scaling (\(q\)-differences) |
| 34B18 | Positive solutions to nonlinear boundary value problems for ordinary differential equations |
| 34A08 | Fractional ordinary differential equations |
Keywords:
fractional \(q\)-difference equations; integral boundary conditions; positive solutions; Green’s function; monotone iterative methodReferences:
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