Attractivity and global attractivity for system of fractional functional and nonlinear fractional q-differential equations

Abstract

In the current work, we present some innovative solutions for the attractivity of fractional functional q-differential equations involving Caputo fractional q-derivative in a $k$-dimensional system, by using some fixed point principle and the standard Schauder's fixed point theorem. Likewise, we look into the global attractivity of fractional q-differential equations involving classical Riemann-Liouville fractional q-derivative in a $k$-dimensional system, by employing the famous  fixed point theorem of Krasnoselskii. Also, we must note that, this paper is mainly on the analysis of the model, with numerics used only to verify the analysis for checking the attractivity and global attractivity of solutions in the system. Lastly, we give two examples to illustrate our main results.