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

Yıl 2020, Cilt: 2 Sayı: 1, 44 - 48, 30.07.2020

Ali Kurt , Orkun Taşbozan

Öz

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.

Anahtar Kelimeler

q-calculus, (B; q)-derivative, (B; q)-integral

Kaynakça

• K.B. Oldham and J. Spanier, The Fractional Calculus, Academic, New York, 1974.
• 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.
• A.Atangana, S.C.O. Noutchie, Model of Break-Bone Fever via Beta-Derivatives, BioMed Research Internationa, 2014, 10 pages, 2014.
• V. Kac and P. Cheung, Quantum Calculus, Springer, New York (2002).
• 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.