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Fuzzy q-Taylor Theorem | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 13، دوره 16، شماره 8، آبان 2025، صفحه 161-178 اصل مقاله (4.14 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2021.23034.2465 | ||
| نویسندگان | ||
| Zahra Noeiaghdam1؛ Morteza Rahmani2؛ Tofigh Allahviranloo* 3 | ||
| 1Department of Mathematics, Shahed University, Tehran, Iran | ||
| 2Faculty of Basic and Advanced Technologies in Biology, University of Science and Culture, Tehran, Iran | ||
| 3Quantum Technologies Research Center, (QTRC), Science and Research Branch, Islamic Azad University, Tehran 1477893855, Iran | ||
| تاریخ دریافت: 14 بهمن 1399، تاریخ پذیرش: 31 فروردین 1400 | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Generalized Hukuhara $q$-difference؛ $q$-Taylor's expansion؛ Fuzzy $q$-derivative؛ Fuzzy $q$-integral؛ Fuzzy $q$-Taylor | ||
| مراجع | ||
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