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http://dx.doi.org/10.14317/jami.2018.271

A RESERCH ON NONLINEAR (p, q)-DIFFERENCE EQUATION TRANSFORMABLE TO LINEAR EQUATIONS USING (p, q)-DERIVATIVE

ROH, KUM-HWAN (Department of Mathematics, Hannam University)
LEE, HUI YOUNG (Department of Mathematics, Hannam University)
KIM, YOUNG ROK (Department of Mathematics, Hannam University)
KANG, JUNG YOOG (Department of Information and Statistics, Anyang University)

Publication Information

Journal of applied mathematics & informatics / v.36, no.3_4, 2018 , pp. 271-283 More about this Journal

Abstract

In this paper, we introduce various first order (p, q)-difference equations. We investigate solutions to equations which are linear (p, q)-difference equations and nonlinear (p, q)-difference equations. We also find some properties of (p, q)-calculus, exponential functions, and inverse function.

Keywords

(p, q)-number; (p, q)-difference equation; (p,q)-exponential function; (p, q)-derivative operator; (p, q)- integral;

Citations & Related Records

Reference

1	M. Arik, E. Demircan, T. Turgut, L. Ekinci, M. Mungan, Fibonacci oscillators, Z. Phys. C:particles and Fields 55 (1992), 89-95. DOI
2	G. Brodimas, A. Jannussis, R. Mignani, Two-parameter quantum groups, Universita di Roma Preprint, Nr. 820 (1991).
3	G. Bangerezako, An introduction to q-difference equations, MIRAMARE-TRIESTE, (2011), https://www.uclouvain.be/cps/ucl/doc/math/documents/RAPSEM354.
4	R.D. Carmichael, The general theory of linear q-qifference equations, Am. J. Math 34 (1912), 147-168. DOI
5	R. Chakrabarti, R. Jagannathan, A (p, q)-oscillator realization of two-parameter quantum algebras, J. Phys. A:Math. Gen. 24 (1991), L711. DOI
6	R.B. Corcino, On P,Q-Binomial coefficients, Electron. J. Combin. Number Theory 8 (2008), A29.
7	T.E. Mason, On properties of the solution of linear q-difference equations with entire function coefficients, Am. J. Math 37 (1915), 439-444. DOI
8	R. Jagannathan, K.S. Rao, Two-parameter quantum algebras, twin-basic numbers, and associasted generalized hypergeometric series, arXiv:math/0602613[math.NT].
9	H.F. Jackson, q-Difference equations, Am. J. Math 32 (1910), 305-314. DOI
10	P.N. Sadjang, On the fundamental theorem of (p, q)-calculus and some (p, q)-Taylor formulas, arXiv:1309.3934[math.QA].
11	W.J. Trjitzinsky, Analytic theory of linear q-difference equations, Acta Mathematica, (1933).
12	M. Wachs, D. White, p, q-Stirling numbers and set partition statistics, J. Combin. Theory A 56 (1991), 27-46. DOI