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Introduction of fuzzy q-fractional derivative and its properties | ||
| Journal of New Researches in Mathematics | ||
| دوره 7، شماره 34، خرداد و تیر 2022، صفحه 125-140 اصل مقاله (322.84 K) | ||
| نوع مقاله: research paper | ||
| نویسندگان | ||
Naser Mikael Vand 1؛ Zahra Noeiaghdam  2
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| 1Department of Mathematics, Islamic Azad University, Ardabil Branch, Ardabil, Iran. | ||
| 2Faculty of Mathematical and Computer Sciences, Shahid University, Tehran, Iran | ||
| چکیده | ||
| The quantum calculus or q-calculus begins with F. H. Jackson in the early twentieth century, but only recently it has aroused interest, due to high demand of mathematics that is modeling quantum computing and it has been an important subject for applied sciences . The quantum calculus is one of the applied and inter disciplinary sciences, which is more important than the classical calculus because in the standard calculus the definition of the derivative depends on the existence of limit but the quantum derivative in quantum calculus works without the definition of limit and for this reason the work with a quantum calculus is numerically faster and easier than the standard calculus. In this paper, fuzzy quantum derivative, fuzzy quantum fractional derivative in Caputo sense by using generalized Hukuhara difference and fuzzy quantum fractional integral of the Riemann-Liouville type are introduced, then the related theorems and properties are provided in details.These results occur in many applications as physics, quantum theory, number theory, statistical mechanics, etc. | ||
| کلیدواژه‌ها | ||
| Generalized Hukuhara difference؛ Quantum calculus؛ Fuzzy q-derivative؛ Fuzzy Caputo q-fractional derivative؛ Fuzzy Riemann-Liouville q-fractional integral | ||
| مراجع | ||
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