Introduction of the numerical methods in quantum calculus with uncertainty

Document Type : Research Article


1 Department of Mathematics, Shahed University, Tehran, Iran

2 Department of Mathematics, Shahed University, Tehran, Iran & 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 & Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran


The aim of this study is the introduction of the numerical methods for solving the fuzzy $q$-differential equations that many real life problems can be modelized in the form of these equations. $q$-Taylor's expansion method is among important and famous methods for solving these problems. In this paper, applications of the fuzzy $q$-Taylor's expansion, the fuzzy local $q$-Taylor's expansion and the fuzzy $q$-Euler's method, based on the generalized Hukuhara $q$-differentiability are illustrated which are two numerical methods for finding approximate solution of the fuzzy initial value $q$-problems (for short FIVq-Ps).