Fuzzy q-Taylor Theorem

Document Type : Research Paper

Authors

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

10.22075/ijnaa.2021.23034.2465

Abstract

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.

Keywords


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