Fuzzy q-Taylor Theorem

Document Type : Research Paper


1 Department of Mathematics, Shahed University, Tehran, Iran

2 Faculty of Basic and Advanced Technologies in Biology, University of Science and Culture, Tehran, Iran

3 Bahcesehir University, Faculty of Engineering and Natural Sciences, Istanbul, Turkey

4 Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran



The main purpose of this work is to introduce and investigate fuzzy quantum calculus. The beginning of our idea is with a general definition of fuzzy $q$-derivative on arbitrary time scales by using the generalized Hukuhara difference. It compiled some basic facts in the fields of the fuzzy $q$-derivative and the fuzzy $q$-integral and proved them in detail. Proceed with this work, specifying the particular concept of fuzzy $q$-Taylor's expansion, especially for continuous and fuzzy valued functions which are non-differentiable in the classical (usual) concept, as the best tool for approximating functions and solving the fuzzy initial value $q$-problems. Eventually, some numerical examples of fuzzy $q$-Taylor's expansion of special functions and functions that have switching points, are solved for illustration.


Articles in Press, Accepted Manuscript
Available Online from 08 September 2023
  • Receive Date: 10 January 2021
  • Revise Date: 02 April 2021
  • Accept Date: 20 April 2021