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Dergiler / Ikonion Journal of Mathematics / 2026 / Volume: 2 Issue: 1

A New Concept for Fractional Quantum Calculus: ( B; q)-Calculus and Its Properties

Ali Kurt(PAMUKKALE UNIVERSITY)
Orkun Taşbozan(HATAY MUSTAFA KEMAL ÜNİVERSİTESİ)
Sayfa
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Yayın Tarihi
2020-07-30
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

These new defi nitions can be used in many different models arising in physical applications.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:In this article, authors expressed a new de finition called (B ; q)- derivative and integral which is a new type of fractional quantum derivative and integral.
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Temel Bulgular & Veri:Also theorems and proofs on some basic properties of (B ; q)- derivative and integral such as product rule, quotient rule, linearity and etc. are stated.
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Sonuç & Katkı:These new defi nitions can be used in many different models arising in physical applications.
🔬Tür:Modelleme & Sayısal Simülasyon
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:q-calculus · q)-derivative · q)-integral

Abstract

In this article, authors expressed a new de finition called (B ; q)- derivative and integral which is a new type of fractional quantum derivative and integral. Also theorems and proofs on some basic properties of (B ; q)- derivative and integral such as product rule, quotient rule, linearity and etc. are stated. These new defi nitions can be used in many different models arising in physical applications.

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Bu Makaleye Atıf Yap

Kurt, A., Taşbozan, O. (2020). A New Concept for Fractional Quantum Calculus: ( B; q)-Calculus and Its Properties. Ikonion Journal of Mathematics, Volume: 2 Issue: 1. https://ajindex.com/articles/1492824

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Kaynakça (5)

  1. K.B. Oldham and J. Spanier, The Fractional Calculus, Academic, New York, 1974.
  2. I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999. A.A. Kilbas, H.M. Srivastava and J.J. Trujillo, Theory and Applications of Fractional Differential Equations. Elsevier, Amsterdam, 2006.
  3. A.Atangana, S.C.O. Noutchie, Model of Break-Bone Fever via Beta-Derivatives, BioMed Research Internationa, 2014, 10 pages, 2014.
  4. V. Kac and P. Cheung, Quantum Calculus, Springer, New York (2002).
  5. J. Tariboon and S.K. Ntouyas, Quantum calculus on nite intervals and applications to impulsive difference equations, Advances in Difference Equations, 282, 1-19, 2013.