On Riemann‐Liouville fractional qq –difference equations and their application to retarded logistic type model

摘要

> In this note, we study a type of nonlinear Riemann‐Liouville fractional q –difference equations. By using the Krasnoselskii fixed‐point theorem, we investigate the existence of solutions of the addressed equation. Prior to the main results and unlike previous theorems, we provide the variation of parameters formula in case the solution starts at some a 0, which belongs to the quantum time scale T q where the solution is only defined. The case when the solution starts at a =0 is also considered. To apply our result, we provide an existence theorem for the Riemann‐Liouville fractional q –logistic type model.