Etemad, SinaNtouyas, Sotiris K.Imran, AtikaHussain, AzharBaleanu, DumitruRezapour, Shahram2022-03-222022-03-222021Etemad, Sina...et al. (2021). "Application of some special operators on the analysis of a new generalized fractional Navier problem in the context of q-calculus", Advances in Difference Equations, Vol. 2021, No. 1.1687-1847http://hdl.handle.net/20.500.12416/5160The key objective of this study is determining several existence criteria for the sequential generalized fractional models of an elastic beam, fourth-order Navier equation in the context of quantum calculus (q-calculus). The required way to accomplish the desired goal is that we first explore an integral equation of fractional order w.r.t. q-RL-integrals. Then, for the existence of solutions, we utilize some fixed point and endpoint conditions with the aid of some new special operators belonging to operator subclasses, orbital alpha-admissible and alpha-psi-contractive operators and multivalued operators involving approximate endpoint criteria, which are constructed by using aforementioned integral equation. Furthermore, we design two examples to numerically analyze our results.eninfo:eu-repo/semantics/openAccessQ-Navier ProblemElastic BeamEndpointFixed PointSpecial OperatorsArticle2021110.1186/s13662-021-03558-8