TY  - JOUR
T1  - ${q}_{k}-$Laplace Transform on Quantum Integral
AU  - Yılmaz, Emrah
AU  - Yılmazer, Mehmet Çağrı
AU  - Göktaş, Sertaç
AU  - Et, Mikail
PY  - 2024
DA  - June
DO  - 10.47000/tjmcs.1343335
JF  - Turkish Journal of Mathematics and Computer Science
JO  - TJMCS
PB  - Matematikçiler Derneği
WT  - DergiPark
SN  - 2148-1830
SP  - 103
EP  - 118
VL  - 16
IS  - 1
LA  - en
AB  - In this study, we present $q_{k}-$Laplace transform by $q_{k}-$integral on quantum analogue. We give some properties of $q_{k}-$Laplace transform. The $q_{k}-$Laplace transforms of some common functions are calculated.
KW  - Laplace transformation
KW  - $q-$calculus
KW  - ${q}_{k}-$calculus
CR  - Abdi, W.H., Certain inversion and representation formulae for q−Laplace transforms, Mathematische Zeitschrift, 83(1964), 238–249.
CR  - Abdulazeez, S.T., Modanli, M. Analytic solution of fractional order Pseudo-Hyperbolic Telegraph equation using modified double Laplace transform method, International Journal of Mathematics and Computer in Engineering, 1(2023), 105–114.
CR  - Adams, C.R., On the linear ordinary q−difference equation, Annals of mathematics, (1928), 195–205.
CR  - Ahmad, B., Boundary-value problems for nonlinear third-order q−difference equations, Electronic Journal of Differential Equations, 94(2011), 1–7.
CR  - Ahmad, B., Alsaedi, A., Ntouyas, S.K., A study of second-order q−difference equations with boundary conditions, Advances in difference equations, 35(2012), 1–10.
CR  - Ahmad, B., Alsaedi, A., Ntouyas, S.K., Tariboon, J., Alzahrani, F., Nonlocal boundary value problems for impulsive fractional qk-difference equations, Advances in Difference Equations, 124(2016), 1–16.
CR  - Ahmad, B., Ntouyas, S.K., Tariboon, J., Quantum Calculus: New Concepts, Impulsive IVPs and BVPs, Inequalities, New York, World Scientific, 2016.
CR  - Alp, N., Sarıkaya, M.Z., q−Laplace transform on quantum integral, Kragujevac Journal of Mathematics, 47(2023) 153–164.
CR  - Alp, N., Sarıkaya, M. Z., A new definition and properties of quantum integral which calls q−integral, Konuralp Journal of Mathematics, 5(2017), 146–159.
CR  - Bangerezako, G., Variational q−calculus, Journal of Mathematical Analysis and Applications, 289(2004), 650–665.
CR  - Bohner, M., Guseinov, G.Sh., The h−Laplace and q−Laplace transforms, Journal of Mathematical Analysis and Applications, 365(2010), 75–92.
CR  - Bohner, M, Hudson, T., Euler-type boundary value problems in quantum calculus, International Journal of Applied Mathematics and Statistics, 9(2007), 19–23.
CR  - Bohner, M, Peterson, A, Dynamic Equations on Time Scales: An Introduction with Applications. Birkh¨auser, Boston, 2001.
CR  - Carmichael, R.D., The general theory of linear q−difference equations, American journal of mathematics, 34(1912), 147–168.
CR  - Cieslinski, J.L., Improved q−exponential and q−trigonometric functions, Applied Mathematics Letters, 24(2011), 2110–2114.
CR  - Chung, W. S., Kim, T., Kwon, H.I., On the q−analog of the Laplace transform, Russian Journal of Mathematical Physics, 21(2014), 156–168.
CR  - Dennis, G.Z., Advanced Engineering Mathematics, Jones & Bartlett Publishers, 2020.
CR  - Diaz, R., Teruel, C., qk-Generalized Gamma and Beta Functions, Journal of Nonlinear Mathematical Physics, 12(2005), 118–134.
CR  - Jackson, F., q−Form of Taylor’s theorem, Messenger of Mathematics, 39(1909), 62–64.
CR  - Jackson, F.H., On q−definite integrals, Quarterly Journal of Pure and Applied Mathematics, 41(1910), 193–203.
CR  - Kac, V., Cheung, P., Quantum Calculus, New York, Springer, 2002.
CR  - Rajkovic, P.M., Stankovic, M.S., Marinkovic, S. D. The zeros of polynomials orthogonal with respect to q-integral on several intervals in the complex plane, In Proceedings of The Fifth International Conference on Geometry, Integrability and Quantization Vol. 5(2004), 178–189.
CR  - Sudsutad, W., Ntouyas, S.K., Tariboon, J., Quantum integral inequalities for convex functions, Journal of Mathematical Inequalities, 9(2015), 781–793.
CR  - Tariboon, J., Ntouyas, S.K., Quantum calculus on finite intervals and applications to impulsive difference equations, Advances in Difference Equations, 282(2013), 1–19.
CR  - Tariboon, J.i Ntouyas, S.K., Quantum integral inequalities on finite intervals, Journal of Inequalities and Applications, 121(2014).
CR  - Trjitzinsky, W.J., Analytic theory of linear q− difference equations, Acta mathematica, 61(1933), 1–38.
CR  - Uçar, F., Albayrak, D., On q−Laplace type integral operators and their applications, Journal of Difference Equations and Applications, 18(2012), 1001–1014.
CR  - Yilmaz, E., Goktas, S., On the solution of a Sturm-Liouville problem by using Laplace transform on time scales, Cumhuriyet Science Journal, 42(2021), 132–140.
CR  - Yu, C, Wang, J., Existence of solutions for nonlinear second-order q−difference equations with first-order q−derivatives, Advances in Difference Equations, 124(2013), 1–11.
UR  - https://doi.org/10.47000/tjmcs.1343335
L1  - https://dergipark.org.tr/en/download/article-file/3333053
ER  -