Application of some special operators on the analysis of a new generalized fractional Navier problem in the context of q-calculus

Etemad S., Ntouyas S. K., Imran A., Hussain A., Baleanu D., Rezapour S.

Advances in Difference Equations, vol.2021, no.1, 2021 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 2021 Issue: 1
  • Publication Date: 2021
  • Doi Number: 10.1186/s13662-021-03558-8
  • Journal Name: Advances in Difference Equations
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Keywords: Elastic beam, Endpoint, Fixed point, q-Navier problem, Special operators
  • Uşak University Affiliated: No

Abstract

The 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 α-admissible and α-ψ-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.