International Journal of Nonlinear Analysis and Applications

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 Quantum Technologies Research Center, (QTRC), Science and Research Branch, Islamic Azad University, Tehran 1477893855, Iran

Abstract

The main purpose of this work is to introduce and investigate fuzzy quantum calculus. Our idea begins with a general definition of fuzzy $q$-derivative on arbitrary time scales 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 with switching points, are solved for illustration.

Keywords

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International Journal of Nonlinear Analysis and Applications
Volume 16, Issue 8
August 2025
Pages 161-178
  • Receive Date: 02 February 2021
  • Accept Date: 20 April 2021