Araştırma Makalesi
BibTex RIS Kaynak Göster

Yıl 2020, Cilt: 49 Sayı: 6, 2046 - 2062, 08.12.2020

Ahmet Daşdemir Tuncay Deniz Şentürk Zafer Ünal

https://doi.org/10.15672/hujms.536435
Cited By: 1

Öz

Kaynakça

  • [1] H. Bulut, Y. Pandir, and H.M. Baskonus, Symmetrical hyperbolic Fibonacci function solutions of generalized Fisher equation with fractional order, AIP Conf. Proc. 1558 (1), 1914–1918, 2013.
  • [2] S.M. Ege and E. Misirli, The modified Kudryashov method for solving some fractional-order nonlinear equations, Adv. Differ. Equ. 2014, Art. No. 135, 2014.
  • [3] S. Falcón and Á. Plaza, On the Fibonacci k-numbers, Chaos Solitons Fractals, 32 (5), 1615–1624, 2007.
  • [4] S. Falcón and Á. Plaza, The k-Fibonacci hyperbolic functions, Chaos Solitons Fractals, 38 (2), 409–420, 2008.
  • [5] A.F. Horadam, A generalized Fibonacci sequence, Amer. Math. Monthly, 68 (5), 455– 459, 1961.
  • [6] A.F. Horadam, Generating functions for powers of a certain generalized sequence of numbers, Duke. Math. J. 32 (3), 437–446, 1965.
  • [7] A.F. Horadam, Basic properties of a certain generalized sequence of numbers, Fibonacci Quart. 3 (3), 161–176, 1965.
  • [8] A.F. Horadam, Special properties of the sequence ${W_n}\left( {a,b;p,q} \right)$, Fibonacci Quart. 5 (3), 424–434, 1967.
  • [9] T. Koshy, Fibonacci and Lucas Numbers with Applications, John Wiley and Sons, Inc., Hoboken, NJ, 2019.
  • [10] Y. Pandir, Y. Gurefe, and E. Misirli, A new approach to Kudryashov’s method for solving some nonlinear physical models, Int. J. Phys. Sci. 7 (21), 2860–2866, 2012.
  • [11] S.S. Ray, New analytical exact solutions of time fractional KdV-KZK equation by Kudryashov methods, Chinese Physics B. 25 (4), 040204, 2016.
  • [12] A.P. Stakhov, Hyperbolic Fibonacci and Lucas functions: a new mathematics for the living nature, ITI, Vinnitsa, 2003.
  • [13] A.P. Stakhov and S. Aranson, Hyperbolic Fibonacci and Lucas functions, “Golden” Fibonacci goniometry, Bodnar’s geometry, and Hilbert’s fourth problem, Appl. Math. 2, 74–84, 2011.
  • [14] A.P. Stakhov and B. Rozin, On a new class of hyperbolic functions, Chaos Solitons Fractals, 23, 379–389, 2005.
  • [15] A.P. Stakhov and B. Rozin, The Golden Shofar, Chaos Solitons Fractals, 26 (3), 677-684, 2005.
  • [16] A.P. Stakhov and B. Rozin, The “golden” hyperbolic models of Universe, Chaos Solitons Fractals, 34 (2), 159–171, 2007.
  • [17] A.P. Stakhov and I.S. Tkachenko, Hyperbolic Fibonacci trigonometry, Rep. Ukr. Acad. Sci. 208, 9–14, 1993.

On recursive hyperbolic functions in Fibonacci-Lucas sense

Yıl 2020, Cilt: 49 Sayı: 6, 2046 - 2062, 08.12.2020

Ahmet Daşdemir Tuncay Deniz Şentürk Zafer Ünal

https://doi.org/10.15672/hujms.536435
Cited By: 1

Öz

The hyperbolic Fibonacci and hyperbolic Lucas functions have been introduced before and have been improved to functions of the symmetrical form. In this paper, we generalize the mentioned definitions, which will be called Horadam hyperbolic sine function $ \left( HSF \right) $ and Horadam hyperbolic cosine function $ \left( HCF \right) $. Further, we present many identities and hyperbolic properties of our new definitions.

Anahtar Kelimeler

Horadam hyperbolic function Horadam spiral quasi-sine Horadam function Honsberger formula Vajda’s identity

Kaynakça

  • [1] H. Bulut, Y. Pandir, and H.M. Baskonus, Symmetrical hyperbolic Fibonacci function solutions of generalized Fisher equation with fractional order, AIP Conf. Proc. 1558 (1), 1914–1918, 2013.
  • [2] S.M. Ege and E. Misirli, The modified Kudryashov method for solving some fractional-order nonlinear equations, Adv. Differ. Equ. 2014, Art. No. 135, 2014.
  • [3] S. Falcón and Á. Plaza, On the Fibonacci k-numbers, Chaos Solitons Fractals, 32 (5), 1615–1624, 2007.
  • [4] S. Falcón and Á. Plaza, The k-Fibonacci hyperbolic functions, Chaos Solitons Fractals, 38 (2), 409–420, 2008.
  • [5] A.F. Horadam, A generalized Fibonacci sequence, Amer. Math. Monthly, 68 (5), 455– 459, 1961.
  • [6] A.F. Horadam, Generating functions for powers of a certain generalized sequence of numbers, Duke. Math. J. 32 (3), 437–446, 1965.
  • [7] A.F. Horadam, Basic properties of a certain generalized sequence of numbers, Fibonacci Quart. 3 (3), 161–176, 1965.
  • [8] A.F. Horadam, Special properties of the sequence ${W_n}\left( {a,b;p,q} \right)$, Fibonacci Quart. 5 (3), 424–434, 1967.
  • [9] T. Koshy, Fibonacci and Lucas Numbers with Applications, John Wiley and Sons, Inc., Hoboken, NJ, 2019.
  • [10] Y. Pandir, Y. Gurefe, and E. Misirli, A new approach to Kudryashov’s method for solving some nonlinear physical models, Int. J. Phys. Sci. 7 (21), 2860–2866, 2012.
  • [11] S.S. Ray, New analytical exact solutions of time fractional KdV-KZK equation by Kudryashov methods, Chinese Physics B. 25 (4), 040204, 2016.
  • [12] A.P. Stakhov, Hyperbolic Fibonacci and Lucas functions: a new mathematics for the living nature, ITI, Vinnitsa, 2003.
  • [13] A.P. Stakhov and S. Aranson, Hyperbolic Fibonacci and Lucas functions, “Golden” Fibonacci goniometry, Bodnar’s geometry, and Hilbert’s fourth problem, Appl. Math. 2, 74–84, 2011.
  • [14] A.P. Stakhov and B. Rozin, On a new class of hyperbolic functions, Chaos Solitons Fractals, 23, 379–389, 2005.
  • [15] A.P. Stakhov and B. Rozin, The Golden Shofar, Chaos Solitons Fractals, 26 (3), 677-684, 2005.
  • [16] A.P. Stakhov and B. Rozin, The “golden” hyperbolic models of Universe, Chaos Solitons Fractals, 34 (2), 159–171, 2007.
  • [17] A.P. Stakhov and I.S. Tkachenko, Hyperbolic Fibonacci trigonometry, Rep. Ukr. Acad. Sci. 208, 9–14, 1993.
Toplam 17 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Matematik
Yazarlar

Ahmet Daşdemir 0000-0001-8352-2020

Tuncay Deniz Şentürk 0000-0002-5247-5097

Zafer Ünal 0000-0003-2445-1028

Yayımlanma Tarihi 8 Aralık 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 49 Sayı: 6

Kaynak Göster

APA Daşdemir, A., Şentürk, T. D., & Ünal, Z. (2020). On recursive hyperbolic functions in Fibonacci-Lucas sense. Hacettepe Journal of Mathematics and Statistics, 49(6), 2046-2062. https://doi.org/10.15672/hujms.536435
AMA Daşdemir A, Şentürk TD, Ünal Z. On recursive hyperbolic functions in Fibonacci-Lucas sense. Hacettepe Journal of Mathematics and Statistics. Aralık 2020;49(6):2046-2062. doi:10.15672/hujms.536435
Chicago Daşdemir, Ahmet, Tuncay Deniz Şentürk, ve Zafer Ünal. “On Recursive Hyperbolic Functions in Fibonacci-Lucas Sense”. Hacettepe Journal of Mathematics and Statistics 49, sy. 6 (Aralık 2020): 2046-62. https://doi.org/10.15672/hujms.536435.
EndNote Daşdemir A, Şentürk TD, Ünal Z (01 Aralık 2020) On recursive hyperbolic functions in Fibonacci-Lucas sense. Hacettepe Journal of Mathematics and Statistics 49 6 2046–2062.
IEEE A. Daşdemir, T. D. Şentürk, ve Z. Ünal, “On recursive hyperbolic functions in Fibonacci-Lucas sense”, Hacettepe Journal of Mathematics and Statistics, c. 49, sy. 6, ss. 2046–2062, 2020, doi: 10.15672/hujms.536435.
ISNAD Daşdemir, Ahmet vd. “On Recursive Hyperbolic Functions in Fibonacci-Lucas Sense”. Hacettepe Journal of Mathematics and Statistics 49/6 (Aralık 2020), 2046-2062. https://doi.org/10.15672/hujms.536435.
JAMA Daşdemir A, Şentürk TD, Ünal Z. On recursive hyperbolic functions in Fibonacci-Lucas sense. Hacettepe Journal of Mathematics and Statistics. 2020;49:2046–2062.
MLA Daşdemir, Ahmet vd. “On Recursive Hyperbolic Functions in Fibonacci-Lucas Sense”. Hacettepe Journal of Mathematics and Statistics, c. 49, sy. 6, 2020, ss. 2046-62, doi:10.15672/hujms.536435.
Vancouver Daşdemir A, Şentürk TD, Ünal Z. On recursive hyperbolic functions in Fibonacci-Lucas sense. Hacettepe Journal of Mathematics and Statistics. 2020;49(6):2046-62.

Cited By

The stability of resource and environmental economics model based on hyperbolic sine function
Applied Mathematics and Nonlinear Sciences
https://doi.org/10.2478/amns.2023.1.00050

https://dergipark.org.tr/en/pub/hujms