Fuzzy q-Taylor Theorem
نویسندگان
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
doi
10.22075/ijnaa.2021.23034.2465چکیده
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.
