Knowledge for the future: Fractional quantum calculus (Calculus without limit) Thanin Sitthiwirattham

Main Article Content

Thanin Sitthiwirattham


This article introduces some different types of fractional quantum calculus: difference calculus, q- calculus and Hahn calculus. By expressing the concept and operator construction of each fractional quantum calculus.


Download data is not yet available.

Article Details

How to Cite
Sitthiwirattham, T. (2021). Knowledge for the future: Fractional quantum calculus (Calculus without limit): Thanin Sitthiwirattham. Journal of Science Innovation for Sustainable Development, 3(1), 1–9. Retrieved from
Invited Paper


Wu G.C., Baleanu D. (2013). Discrete chaos in fractional sine and standard maps. Phys. Lett. A., 378, 484-487.

Wu G.C., Baleanu D. (2014). Discrete fractional logistic map and its chaos. Nonlinear Dyn., 75, 283-287.

Wu G.C., Baleanu D. (2014). Chaos synchronization of the discrete fractional logistic map. Signal Process., 102, 96–99.

Wu G.C., Baleanu D., Zeng S.D., Deng Z.G. (2015). Discrete fractional diffusion equation. Nonlinear Dyn., 80 (1–2), 281–286.

Diaz J.B., Olser T.J. (1974). Differences of Fractional Order, Math. Comput., 28, 185-202.

Miller K.S., Ross B. (1989) Fractional difference calculus, in Proceedings of the International Symposium on Univalent Functions, Fractional Calculus, and Their Applications, Nihon University, Koriyama, Japan, 1989, 139–152.

Anastassiou G.A. Discrete fractional calculus and inequalities,

Gray H.L., Zhang N.F. (1988). On a new definition of the fractional difference, Math. Comput., 50:182, 513–529.

Hirota R. (2000). Lectures on Difference Equations, Science-sha, Tokyo, Japan.

Nagai A. (2003). Discrete Mittag-Leffler function and its applications, new developments in the research of integrable systems: continuous, discrete, ultra-discrete, RIMS Kokyuroku, 1302, 1–20.

Atici F.M., Eloe P.W. (2009). Discrete fractional calculus with the nabla operator, Electron. J. Qual. Theory Differ. Equat., Special Edition I, 2009, 1-12.

Anastassiou G.A. (2010). Nabla discrete fractional calculus and nabla inequalities, Math. Comput. Model, 51, 562–571.

Al-Salam W.A. (1997). Some fractional q-integrals and q-derivative, Proc. Edinb. Math. Soc., 15:2, 135-140.

Agarwal R.P. (1969). Certain fractional q-integral and q-derivatives, Proc. Cambridge Philos. Soc., 66, 365-370.

Čermák J., Nechvatál L., (2010). On q,h - analogue of fractional calculus. J. Nonlinear Math. Phy., 17:1, 51-68.

Čermák J., Kisela T., Nechvatál L. (2011). Discrete Mittag-Leffler Functions in Linear Fractional Difference Equations. Abstr. Appl. Anal., Article ID 565067, 21 pages.

Brikshavana T., Sitthiwirattham T. (2017). On fractional Hahn calculus with the delta operators. Adv. Differ. Equ., 2017:354.

Patanarapeelert, N., Sitthiwirattham, T. (2019). On Fractional Symmetric Hahn Calculus Mathematics, 7, 873.

Soontraranon, J., Sitthiwirattham, T. (2020). On Fractional (p,q) - Calculus. Adv. Differ. Equ., 2020:35.