On a fractional cantilever beam model in the q-difference inclusion settings via special multi-valued operators - Etemad, Sina; Hussain, Azhar; Imran, Atika; Alzabut, Jehad; Rezapour, Shahram; Selvam, A. George Maria (Journal of inequalities and applications, 2021)
The fundamental goal of the study under consideration is to establish some of the existence criteria needed for a particular fractional inclusion model of cantilever beam in the setting of quantum calculus using new arguments of existence theory. In this way, we investigate a fractional integral equation that corresponds to the aforementioned boundary value problem. In a more concrete sense, we design new multi-valued operators based on this integral equation, which belong to the certain subclasses of functions, called α -admissible and α - ψ -contractive multi-functions, in combination with the AEP-property. Also, we use some inequalities such as Ω-inequality and set-valued version inequalities. Moreover, we add a simulative example for a numerical analysis of our results obtained in this study.