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Amleh A. M., Grove E. A., Georgiou D. A., (1999), On the recursive sequence
xn+1=α+xn−1xn{x_{n + 1}} = \alpha + {{{x_{n - 1}}} \over {{x_n}}}
, J. Math. Anal. Appl.AmlehA. M.GroveE. A.GeorgiouD. A.1999On the recursive sequence
xn+1=α+xn−1xn{x_{n + 1}} = \alpha + {{{x_{n - 1}}} \over {{x_n}}}10.1006/jmaa.1999.6346Search in Google Scholar
Amleh A. M., Kirk, V., Ladas G., (2001), On the dynamics of
A+α+bxn−1A+Bxn−2A + {{\alpha + {bx_{n - 1}}} \over {A + {Bx_{n - 2}}}}
, Math Sci. Res. Hot-Line.AmlehA. M.KirkV.LadasG.2001On the dynamics of
A+α+bxn−1A+Bxn−2A + {{\alpha + {bx_{n - 1}}} \over {A + {Bx_{n - 2}}}}Search in Google Scholar
Cinar C., (2004), On the positive solutions of the difference equation
xn+1=xn−11+αxnxn−1{x_{n + 1}} = {{{x_{n - 1}}} \over {1 + \alpha {x_n}{x_{n - 1}}}}
, J. Appl. Math.Comput.CinarC.2004On the positive solutions of the difference equation
xn+1=xn−11+αxnxn−1{x_{n + 1}} = {{{x_{n - 1}}} \over {1 + \alpha {x_n}{x_{n - 1}}}}10.1016/S0096-3003(03)00194-2Search in Google Scholar
Cinar C., (2004), On the positive solutions of the difference equation
xn+1=xn−1−1αxnxn−1{x_{n + 1}} = {{{x_{n - 1}}} \over { - 1\alpha {x_n}{x_{n - 1}}}}
, Appl. Math. Comput.CinarC.2004On the positive solutions of the difference equation
xn+1=xn−1−1αxnxn−1{x_{n + 1}} = {{{x_{n - 1}}} \over { - 1\alpha {x_n}{x_{n - 1}}}}10.1016/S0096-3003(03)00194-2Search in Google Scholar
Cinar C., (2004), On the positive solutions of the difference equation
xn+1=αxn−11+bxnxn−1{x_{n + 1}} = {{\alpha {x_{n - 1}}} \over {1 + {bx_n}{x_{n - 1}}}}
, Appl. Math. Comput.CinarC.2004On the positive solutions of the difference equation
xn+1=αxn−11+bxnxn−1{x_{n + 1}} = {{\alpha {x_{n - 1}}} \over {1 + {bx_n}{x_{n - 1}}}}Search in Google Scholar
DeVault R., Ladas G. and Schultz S. W., (1998), On the recursive sequence
xn+1=Axn+1xn−2{x_{n + 1}} = {A \over {{x_n}}} + {1 \over {{x_{n - 2}}}}
, Proc. Amer. Math. Soc. 24 Dagistan Simsek, Burak Ogul and Fahreddin Abdullayev. Applied Mathematics and Nonlinear Sciences 1(2015) 15–24DeVaultR.LadasG.SchultzS. W.1998On the recursive sequence
xn+1=Axn+1xn−2{x_{n + 1}} = {A \over {{x_n}}} + {1 \over {{x_{n - 2}}}}24 Dagistan Simsek, Burak Ogul and Fahreddin Abdullayev. Applied Mathematics and Nonlinear Sciences 1(2015) 15–24Search in Google Scholar
El-Owaidy, H. M., Ahmed, A. M., Mousa, M. S., (2003), On the recursive sequences
xn+1=αxn−1β±xn{x_{n + 1}} = {{\alpha {x_{n - 1}}} \over {\beta \pm {x_n}}}
, J. Appl. Math. Comput., 145, 747–753.El-OwaidyH. M.AhmedA. M.MousaM. S.2003On the recursive sequences
xn+1=αxn−1β±xn{x_{n + 1}} = {{\alpha {x_{n - 1}}} \over {\beta \pm {x_n}}}14574775310.1016/S0096-3003(03)00271-6Search in Google Scholar
El-Owaidy, H. M., Ahmed, A. M., Elsady, Z., (2004), Global attractivity of the recursive sequences
xn+1=α−βxn−1γ+xn{x_{n + 1}} = {{\alpha - \beta {x_{n - 1}}} \over {\gamma + {x_n}}}
, J. Appl. Math. Comput., Vol:151, 827–833.El-OwaidyH. M.AhmedA. M.ElsadyZ.2004Global attractivity of the recursive sequences
xn+1=α−βxn−1γ+xn{x_{n + 1}} = {{\alpha - \beta {x_{n - 1}}} \over {\gamma + {x_n}}}15182783310.1016/S0096-3003(03)00539-3Search in Google Scholar
Elabbasy E. M., El-Metwally H., Elsayed E. M., (2006), On the difference equation
xn+1=αxn−bxncxn−dxn−1{x_{n + 1}} = \alpha {x_n} - {{{bx_n}} \over {c{x_n} - {dx_{n - 1}}}}
, Advances in Difference Equation, 1–10.ElabbasyE. M.El-MetwallyH.ElsayedE. M.2006On the difference equation
xn+1=αxn−bxncxn−dxn−1{x_{n + 1}} = \alpha {x_n} - {{{bx_n}} \over {c{x_n} - {dx_{n - 1}}}}11010.1155/ADE/2006/82579Search in Google Scholar
Elabbasy E. M., El-Metwally H., Elsayed E. M., (2007), On the difference equation
xn+1=αxn−kβ+γ∏i=0kxn−i{x_{n + 1}} = {{\alpha {x_{n - k}}} \over {\beta + \gamma \prod\nolimits_{i = 0}^k {x_{n - i}}}}
, J. Conc. Appl. Math., 5(2), 101–113.ElabbasyE. M.El-MetwallyH.ElsayedE. M.2007On the difference equation
xn+1=αxn−kβ+γ∏i=0kxn−i{x_{n + 1}} = {{\alpha {x_{n - k}}} \over {\beta + \gamma \prod\nolimits_{i = 0}^k {x_{n - i}}}}52101113Search in Google Scholar
Elabbasy E. M., El-Metwally H., Elsayed E. M., (2007), Qualitative behavior of higher order difference equation, Soochow Journal of Mathematics, 33(4), 861–873.ElabbasyE. M.El-MetwallyH.ElsayedE. M.2007Qualitative behavior of higher order difference equation334861873Search in Google Scholar
Elabbasy E. M., El-Metwally H., Elsayed E. M., (2007), Global attractivity and periodic character of a fractional difference equation of order three, Yokohama Mathematical Journal, 53, 89–100.ElabbasyE. M.El-MetwallyH.ElsayedE. M.2007Global attractivity and periodic character of a fractional difference equation of order three5389100Search in Google Scholar
Elabbasy E. M. and Elsayed E. M., (2008), Global attractivity of difference equation of higher order, Carpathian Journal of Mathematics, 24(2), 45–53.ElabbasyE. M.ElsayedE. M.2008Global attractivity of difference equation of higher order2424553Search in Google Scholar
Elaydi, S., (1996), An Introduction to Difference Equations, Spinger-Verlag, New York.ElaydiS.1996Spinger-VerlagNew York10.1007/978-1-4757-9168-6Search in Google Scholar
Elsayed E. M., (2008), On the solution of recursive sequence of order two, Fasciculi Mathematici, 40, 5–13.ElsayedE. M.2008On the solution of recursive sequence of order two40513Search in Google Scholar
Elsayed E. M., (2009), Dynamics of a rational recursive sequences, International Journal of Difference Equations, 4(2), 185–200.ElsayedE. M.2009Dynamics of a rational recursive sequences42185200Search in Google Scholar
Elsayed E. M., (2009), Dynamics of a Recursive Sequence of Higher Order, Communications on Applied Nonlinear Analysis, 16(2), 37–50.ElsayedE. M.2009Dynamics of a Recursive Sequence of Higher Order1623750Search in Google Scholar
Elsayed E. M., (2011), Solution and atractivity for a rational recursive sequence, Discrete Dynamics in Nature and Society, 17–30.ElsayedE. M.2011Solution and atractivity for a rational recursive sequence173010.1155/2011/982309Search in Google Scholar
Elsayed E. M., (2011), On the solution of some difference equation, Europan Journal of Pure and Applied Mathematics, 4(3), 287–303.ElsayedE. M.2011On the solution of some difference equation43287303Search in Google Scholar
Elsayed E. M., (2012), On the Dynamics of a higher order rational recursive sequence, Communications in Mathematical Analysis, 12(1), 117–133.ElsayedE. M.2012On the Dynamics of a higher order rational recursive sequence12111713310.1186/1687-1847-2012-69Search in Google Scholar
Elsayed E. M., (2012), Solution of rational difference system of order two, Mathematical and Computer Modelling, 55, 378–384.ElsayedE. M.2012Solution of rational difference system of order two5537838410.1016/j.mcm.2011.08.012Search in Google Scholar
Elsayed E. M., (2016), Dynamics of a three-dimensional systems of rational difference equations, Mathematical Methods in the Applied Sciences, 39(5), 1026–1038.ElsayedE. M.2016Dynamics of a three-dimensional systems of rational difference equations3951026103810.1002/mma.3540Search in Google Scholar
Elsayed E. M., (2016), Dynamics of behavior of a higher order rational difference equation, The Journal of Nonlinear Science and Applications, 9(4), 1463–1474.ElsayedE. M.2016Dynamics of behavior of a higher order rational difference equation941463147410.22436/jnsa.009.04.06Search in Google Scholar
Elsayed E. M., (2015), New method to obtain periodic solutions of period two and three of a rational difference equation, Nonlinear Dynamics, 79(1), 241–250.ElsayedE. M.2015New method to obtain periodic solutions of period two and three of a rational difference equation79124125010.1007/s11071-014-1660-2Search in Google Scholar
Simsek D., Cinar C., Yalcinkaya I., (2006), On the recursive sequence
xn+1=xn−31+xn−1{x_{n + 1}} = {{{x_{n - 3}}} \over {1 + {x_{n - 1}}}}
, Internat. J. Contemp. 9(12), 475–480.SimsekD.CinarC.YalcinkayaI.2006On the recursive sequence
xn+1=xn−31+xn−1{x_{n + 1}} = {{{x_{n - 3}}} \over {1 + {x_{n - 1}}}}912475480Search in Google Scholar
Simsek D., Cinar C., Karatas R., Yalcinkaya I., (2006), On the recursive sequence
xn+1=xn−51+xn−2{x_{n + 1}} = {{{x_{n - 5}}} \over {1 + {x_{n - 2}}}}
, Int. J. Pure Appl. Math., 27(4), 501–507.SimsekD.CinarC.KaratasR.YalcinkayaI.2006On the recursive sequence
xn+1=xn−51+xn−2{x_{n + 1}} = {{{x_{n - 5}}} \over {1 + {x_{n - 2}}}}274501507Search in Google Scholar
Simsek D., Cinar C., Karatas R., Yalcinkaya I., (2006), On the recursive sequence
xn+1=xn−51+xn−1xn−3{x_{n + 1}} = {{{x_{n - 5}}} \over {1 + {x_{n - 1}}{x_{n - 3}}}}
, Int. J. Pure Appl. Math., 28(1), 117–124.SimsekD.CinarC.KaratasR.YalcinkayaI.2006On the recursive sequence
xn+1=xn−51+xn−1xn−3{x_{n + 1}} = {{{x_{n - 5}}} \over {1 + {x_{n - 1}}{x_{n - 3}}}}281117124Search in Google Scholar
Simsek D., Cinar C., Yalcinkaya I., (2008), On the recursive sequence
xn+1=xn−(5k+9)1+xn−4xn−9xn−(5k+4){x_{n + 1}} = {{{x_{n - (5k + 9)}}} \over {1 + {x_{n - 4}}{x_{n - 9}}{x_{n - (5k + 4)}}}}
Taiwanese Journal of Mathematics, 12(5), 1087–1098.SimsekD.CinarC.YalcinkayaI.2008On the recursive sequence
xn+1=xn−(5k+9)1+xn−4xn−9xn−(5k+4){x_{n + 1}} = {{{x_{n - (5k + 9)}}} \over {1 + {x_{n - 4}}{x_{n - 9}}{x_{n - (5k + 4)}}}}1251087109810.11650/twjm/1500574249Search in Google Scholar
Simsek D., Ogul B., Abdullayev F., (2017), Solutions of the rational difference equations
xn+1=xn−111+xn−2xn−5xn−8{x_{n + 1}} = {{{x_{n - 11}}} \over {1 + {x_{n - 2}}{x_{n - 5}}{x_{n - 8}}}}
, AIP Conference Proceedings 1880(1) 040003.SimsekD.OgulB.AbdullayevF.2017Solutions of the rational difference equations
xn+1=xn−111+xn−2xn−5xn−8{x_{n + 1}} = {{{x_{n - 11}}} \over {1 + {x_{n - 2}}{x_{n - 5}}{x_{n - 8}}}}1880104000310.1063/1.5000619Search in Google Scholar
Simsek D., Abdullayev F., (2017), On the Recursive Sequence
xn+1=αxn−4k+31+∏t=02xn−(k+1)t−k{x_{n + 1}} = {{\alpha {x_{n - 4k + 3}}} \over {1 + \prod\nolimits_{t = 0}^2 {x_{n - (k + 1)t - k}}}}
, Journal of Mathematics Sciences, 222(6), 762–771.SimsekD.AbdullayevF.2017On the Recursive Sequence
xn+1=αxn−4k+31+∏t=02xn−(k+1)t−k{x_{n + 1}} = {{\alpha {x_{n - 4k + 3}}} \over {1 + \prod\nolimits_{t = 0}^2 {x_{n - (k + 1)t - k}}}}222676277110.1007/s10958-017-3330-7Search in Google Scholar
Simsek D., Dogan A., (2014), On A Class of Recursive Sequence, Manas Journal of Engineering, 2(1), 16–22.SimsekD.DoganA.2014On A Class of Recursive Sequence211622Search in Google Scholar
Simsek D., Ogul B., (2017), Solutions of the Rational Difference Equations
xn+1=xn−(2k+1)1+xn−k{x_{n + 1}} = {{{x_{n - (2k + 1)}}} \over {1 + {x_{n - k}}}}
, Manas Journal of Engineering, 5(3), 57–68.SimsekD.OgulB.2017Solutions of the Rational Difference Equations
xn+1=xn−(2k+1)1+xn−k{x_{n + 1}} = {{{x_{n - (2k + 1)}}} \over {1 + {x_{n - k}}}}53576810.1063/1.5000619Search in Google Scholar
Simsek D., Ogul B., (2018), Solutions of the Rational Difference Equations, Manas Journal of Engineering, 6(1), 56–74.SimsekD.OgulB.2018Solutions of the Rational Difference Equations615674Search in Google Scholar