Research Article
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Year 2022, , 136 - 144, 29.12.2022
https://doi.org/10.32323/ujma.1198471

Abstract

References

  • [1] M. Gümüş¸, R. Abo-Zeid, An explicit formula and forbidden set for a higher order difference equation, J. Appl. Math. Comput., 63 (2020), 133-142.
  • [2] R. Abo-Zeid, Forbidden set and solutions of a higher order difference equation, Dyn. Contin. Discrete Impuls. Syst. Ser. B Appl. Algorithms, 25 (2018), 75-84.
  • [3] R. Abo-Zeid, On the solutions of a higher order difference equation, Georgian Math. J., 27(2) (2020), 165-175.
  • [4] R. Abo-Zeid, Solutions of a higher order difference equation, Math. Pannon., 26(2) (2017-2018), 107-118.
  • [5] R. Abo-Zeid, H. Kamal, Global behavior of a third order difference equation with quadratic term, Bol. Soc. Mat. Mex., 27(1) (2021), Article: 23, 15 pages.
  • [6] R. Abo-Zeid, On the solutions of a higher order recursive sequence, Malaya J. Mat., 8 (2020), 695-701.
  • [7] R. Abo-Zeid, Behavior of solutions of a rational third order difference equation, J. Appl. Math. Inform., 38 (1-2) (2020), 1-12.
  • [8] R. Abo-Zeid, Global Behavior of a fourth order difference equation with quadratic term, Bol. Soc. Mat. Mex., 25(1) (2019), 187-194.
  • [9] R. Abo-Zeid, Global behavior of two third order rational difference equations with quadratic terms, Math. Slovaca, 69 (2019), 147-158.
  • [10] R. Abo-Zeid, H. Kamal, Global behavior of two rational third order difference equations, Univers. J. Math. Appl., 2(4) (2019), 212-217.
  • [11] R. Abo-Zeid, On a third order difference equation, Acta Univ. Apulensis, 8 (2018), 89-103.
  • [12] R. Abo-Zeid, Global behavior of a higher order rational difference equation, Filomat, 30(12) (2016), 3265-3276.
  • [13] R. Abo-Zeid, On the solutions of two third order recursive sequences, Armen. J. Math., 6(2) (2014), 64-66.
  • [14] Y. Akrour, N. Touafek, Y. Halim, On systems of difference equations of second order solved in closed-form, Miskolc Math. Notes, 20 (2019), 701-717.
  • [15] M. B. Almatrafi, M. M. Alzubaidi, Analysis of the qualitative behaviour of an eighth-order fractional difference equation, Open J. Discrete Math., 2 (2019), 41-47.
  • [16] M. Berkal, K. Berehal, N. Rezaiki, Representation of solutions of a system of five-order nonlinear difference equations, J. Appl. Math. Inform., 40(3-4) (2022), 409-431.
  • [17] E. M. Elsayed, M. M. El-Dessoky, Dynamics and global behavior for a fourth-order rational difference equation, Hacet. J. Math. Stat., 42 (2013), 479-494.
  • [18] N. Haddad, J. F. T. Rabago, Dynamics of a system of k􀀀difference equations, Elect. J. Math. Anal. Appl., 5 (2017), 242-249.
  • [19] Y. Halim, N. Touafek, Y. Yazlik, Dynamic behavior of a second-order nonlinear rational difference equation, Turkish J. Math., 39 (2015), 1004-1018.
  • [20] Y. Halim, M. Berkal, A. Khelifa, On a three-dimensional solvable system of difference equations, Turkish J. Math., 44 (2020), 1263-1288.
  • [21] Y. Halim, A. Khelifa, M. Berkal, Representation of solutions of a two-dimensional system of difference equations, Miskolc Math. Notes, 21 (2020), 203-218.
  • [22] T. F. ˙Ibrahim, Periodicity and global attractivity of difference equation of higher order, J. Comput. Anal. Appl., 16 (2014), 552-564.
  • [23] M. Kara, Y. Yazlık, D. T. Tollu, Solvability of a system of higher order nonlinear difference equations, Hacet. J. Math. Stat., 49(5) (2020), 1566-1593.
  • [24] A. Khelifa, Y. Halim, M. Berkal, Solutions of a system of two higher-order difference equations in terms of Lucas sequence, Univers. J. Math. Appl., 2 (2019), 202-211.
  • [25] A. Khelifa, Y. Halim, A. Bouchair, M. Berkal, On a system of three difference equations of higher order solved in terms of Lucas and Fibonacci numbers, Math. Slovaca, 70 (2020), 641-656.
  • [26] A. S. Kurbanlı, C. C¸ ınar, I. Yalc¸ınkaya, On the behavior of positive solutions of the system of rational difference equations, Math. Comput. Model., 53 (2011), 1261-1267.
  • [27] S. Stevi´c, Representation of solutions of bilinear difference equations in terms of generalized Fibonacci sequences, Electron. J. Qual. Theory Differ. Equ., 67 (2014), 1-15.
  • [28] S. Stevi´c, M. A. Alghamdi, A. Alotaibi, E. M. Elsayed, On a class of solvable higher-order difference equations, Filomat, 31 (2017), 461-477.

On a Rational $(P+1)$th Order Difference Equation with Quadratic Term

Year 2022, , 136 - 144, 29.12.2022
https://doi.org/10.32323/ujma.1198471

Abstract

In this paper, we derive the forbidden set and determine the solutions of the difference equation that contains a quadratic term \begin{equation*} x_{n+1}=\frac{x_{n}x_{n-p}}{ax_{n-(p-1)}+bx_{n-p}},\quad n\in\mathbb{N}_0, \end{equation*} where the parameters $a$ and $b$ are real numbers, $p$ is a positive integer and the initial conditions $x_{-p}$, $x_{-p+1}$, $\cdots$, $x_{-1}$, $x_{0}$ are real numbers.

References

  • [1] M. Gümüş¸, R. Abo-Zeid, An explicit formula and forbidden set for a higher order difference equation, J. Appl. Math. Comput., 63 (2020), 133-142.
  • [2] R. Abo-Zeid, Forbidden set and solutions of a higher order difference equation, Dyn. Contin. Discrete Impuls. Syst. Ser. B Appl. Algorithms, 25 (2018), 75-84.
  • [3] R. Abo-Zeid, On the solutions of a higher order difference equation, Georgian Math. J., 27(2) (2020), 165-175.
  • [4] R. Abo-Zeid, Solutions of a higher order difference equation, Math. Pannon., 26(2) (2017-2018), 107-118.
  • [5] R. Abo-Zeid, H. Kamal, Global behavior of a third order difference equation with quadratic term, Bol. Soc. Mat. Mex., 27(1) (2021), Article: 23, 15 pages.
  • [6] R. Abo-Zeid, On the solutions of a higher order recursive sequence, Malaya J. Mat., 8 (2020), 695-701.
  • [7] R. Abo-Zeid, Behavior of solutions of a rational third order difference equation, J. Appl. Math. Inform., 38 (1-2) (2020), 1-12.
  • [8] R. Abo-Zeid, Global Behavior of a fourth order difference equation with quadratic term, Bol. Soc. Mat. Mex., 25(1) (2019), 187-194.
  • [9] R. Abo-Zeid, Global behavior of two third order rational difference equations with quadratic terms, Math. Slovaca, 69 (2019), 147-158.
  • [10] R. Abo-Zeid, H. Kamal, Global behavior of two rational third order difference equations, Univers. J. Math. Appl., 2(4) (2019), 212-217.
  • [11] R. Abo-Zeid, On a third order difference equation, Acta Univ. Apulensis, 8 (2018), 89-103.
  • [12] R. Abo-Zeid, Global behavior of a higher order rational difference equation, Filomat, 30(12) (2016), 3265-3276.
  • [13] R. Abo-Zeid, On the solutions of two third order recursive sequences, Armen. J. Math., 6(2) (2014), 64-66.
  • [14] Y. Akrour, N. Touafek, Y. Halim, On systems of difference equations of second order solved in closed-form, Miskolc Math. Notes, 20 (2019), 701-717.
  • [15] M. B. Almatrafi, M. M. Alzubaidi, Analysis of the qualitative behaviour of an eighth-order fractional difference equation, Open J. Discrete Math., 2 (2019), 41-47.
  • [16] M. Berkal, K. Berehal, N. Rezaiki, Representation of solutions of a system of five-order nonlinear difference equations, J. Appl. Math. Inform., 40(3-4) (2022), 409-431.
  • [17] E. M. Elsayed, M. M. El-Dessoky, Dynamics and global behavior for a fourth-order rational difference equation, Hacet. J. Math. Stat., 42 (2013), 479-494.
  • [18] N. Haddad, J. F. T. Rabago, Dynamics of a system of k􀀀difference equations, Elect. J. Math. Anal. Appl., 5 (2017), 242-249.
  • [19] Y. Halim, N. Touafek, Y. Yazlik, Dynamic behavior of a second-order nonlinear rational difference equation, Turkish J. Math., 39 (2015), 1004-1018.
  • [20] Y. Halim, M. Berkal, A. Khelifa, On a three-dimensional solvable system of difference equations, Turkish J. Math., 44 (2020), 1263-1288.
  • [21] Y. Halim, A. Khelifa, M. Berkal, Representation of solutions of a two-dimensional system of difference equations, Miskolc Math. Notes, 21 (2020), 203-218.
  • [22] T. F. ˙Ibrahim, Periodicity and global attractivity of difference equation of higher order, J. Comput. Anal. Appl., 16 (2014), 552-564.
  • [23] M. Kara, Y. Yazlık, D. T. Tollu, Solvability of a system of higher order nonlinear difference equations, Hacet. J. Math. Stat., 49(5) (2020), 1566-1593.
  • [24] A. Khelifa, Y. Halim, M. Berkal, Solutions of a system of two higher-order difference equations in terms of Lucas sequence, Univers. J. Math. Appl., 2 (2019), 202-211.
  • [25] A. Khelifa, Y. Halim, A. Bouchair, M. Berkal, On a system of three difference equations of higher order solved in terms of Lucas and Fibonacci numbers, Math. Slovaca, 70 (2020), 641-656.
  • [26] A. S. Kurbanlı, C. C¸ ınar, I. Yalc¸ınkaya, On the behavior of positive solutions of the system of rational difference equations, Math. Comput. Model., 53 (2011), 1261-1267.
  • [27] S. Stevi´c, Representation of solutions of bilinear difference equations in terms of generalized Fibonacci sequences, Electron. J. Qual. Theory Differ. Equ., 67 (2014), 1-15.
  • [28] S. Stevi´c, M. A. Alghamdi, A. Alotaibi, E. M. Elsayed, On a class of solvable higher-order difference equations, Filomat, 31 (2017), 461-477.
There are 28 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Messaoud Berkal

R Abo-zeıd

Publication Date December 29, 2022
Submission Date November 2, 2022
Acceptance Date December 7, 2022
Published in Issue Year 2022

Cite

APA Berkal, M., & Abo-zeıd, R. (2022). On a Rational $(P+1)$th Order Difference Equation with Quadratic Term. Universal Journal of Mathematics and Applications, 5(4), 136-144. https://doi.org/10.32323/ujma.1198471
AMA Berkal M, Abo-zeıd R. On a Rational $(P+1)$th Order Difference Equation with Quadratic Term. Univ. J. Math. Appl. December 2022;5(4):136-144. doi:10.32323/ujma.1198471
Chicago Berkal, Messaoud, and R Abo-zeıd. “On a Rational $(P+1)$th Order Difference Equation With Quadratic Term”. Universal Journal of Mathematics and Applications 5, no. 4 (December 2022): 136-44. https://doi.org/10.32323/ujma.1198471.
EndNote Berkal M, Abo-zeıd R (December 1, 2022) On a Rational $(P+1)$th Order Difference Equation with Quadratic Term. Universal Journal of Mathematics and Applications 5 4 136–144.
IEEE M. Berkal and R. Abo-zeıd, “On a Rational $(P+1)$th Order Difference Equation with Quadratic Term”, Univ. J. Math. Appl., vol. 5, no. 4, pp. 136–144, 2022, doi: 10.32323/ujma.1198471.
ISNAD Berkal, Messaoud - Abo-zeıd, R. “On a Rational $(P+1)$th Order Difference Equation With Quadratic Term”. Universal Journal of Mathematics and Applications 5/4 (December 2022), 136-144. https://doi.org/10.32323/ujma.1198471.
JAMA Berkal M, Abo-zeıd R. On a Rational $(P+1)$th Order Difference Equation with Quadratic Term. Univ. J. Math. Appl. 2022;5:136–144.
MLA Berkal, Messaoud and R Abo-zeıd. “On a Rational $(P+1)$th Order Difference Equation With Quadratic Term”. Universal Journal of Mathematics and Applications, vol. 5, no. 4, 2022, pp. 136-44, doi:10.32323/ujma.1198471.
Vancouver Berkal M, Abo-zeıd R. On a Rational $(P+1)$th Order Difference Equation with Quadratic Term. Univ. J. Math. Appl. 2022;5(4):136-44.

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