Theoretical analysis of higher-order system of difference equations with generalized balancing numbers

References

[1] Abo-Zeid, R.: Forbidden sets and stability in some rational difference equations, J. Difference Equ. Appl. 24(2) (2018), 220–239.10.1080/10236198.2017.1400023Search in Google Scholar

[2] Abo-Zeid, R.: On a third order difference equation, Acta Univ. Apulensis Math. Inform. 55(1) (2018), 89–103.10.17114/j.aua.2018.55.07Search in Google Scholar

[3] Allam, A.—Halim, Y.—Khelifa, A.: Convergence of solutions of a system of recurrence equations, J. Appl. Math. Comput. 69 (2023), 1659–1677.10.1007/s12190-022-01807-xSearch in Google Scholar

[4] Akrour, Y.—Touafek, N.—Halim, Y.: On a system of difference equations of second order solved in closed-form, Miskolc Math. Notes 20(2) (2019), 701–717.10.18514/MMN.2019.2923Search in Google Scholar

[5] Behera, A.—Panda G. K.: On the square roots of triangular numbers, Fibonacci Quart. 37(2) (1999), 98–105.10.1080/00150517.1999.12428864Search in Google Scholar

[6] Elsayed, E. M.: On a system of two nonlinear difference equations of order two, Proc. Jangjeon Math. Soc. 18(3) (2015), 353–368.Search in Google Scholar

[7] Elsayed, E. M.: Solutions of rational difference systems of order two, Math. Comput. Model. 55(2) (2012), 378–384.10.1016/j.mcm.2011.08.012Search in Google Scholar

[8] Elsayed, E. M.—Ibrahim, T. F.: Periodicity and solutions for some systems of nonlinear rational difference equations, Hacet. J. Math. Stat. 44(1) (2015), 1361–1390.Search in Google Scholar

[9] Gumus, M.—Abo-Zeid, R.: On the solutions of a (2k+2)th order difference equation, Dyn. Contin. Discrete Impuls. Syst. Ser. B Appl. Algorithms 25(1) (2018), 129–143.Search in Google Scholar

[10] Gumus, M.: Analysis of periodicity for a new class of non-linear difference equations by using a new method, Electron. J. Math. Anal. Appl. 8(1) (2020), 109–116.10.21608/ejmaa.2020.312810Search in Google Scholar

[11] Halim, Y.: Global character of systems of rational difference equations, Electron. J. Math. Anal. Appl. 3 (2015), 204–214.10.21608/ejmaa.2015.310711Search in Google Scholar

[12] Halim, Y.: Form and periodicity of solutions of some systems of higher-order difference equations, Math. Sci. Lett. 5 (2016), 79–84.10.18576/msl/050111Search in Google Scholar

[13] Halim, Y.: A system of difference equations with solutions associated to Fibonacci numbers, Int. J. Differ. Equ. 11 (2016), 65–77.Search in Google Scholar

[14] Halim, Y.—Touafek, N.—Yazlik, Y.: Dynamic behavior of a second-order nonlinear rational difference equation, Turkish J. Math. 39 (2015), 1004–1018.10.3906/mat-1503-80Search in Google Scholar

[15] Halim, Y.—Bayram, M.: On the solutions of a higher-order difference equation in terms of generalized Fibonacci sequences, Math. Methods Appl. Sci. 39 (2016), 2974–2982.10.1002/mma.3745Search in Google Scholar

[16] Halim, Y.—Rabago, J. F. T.: On some solvable systems of difference equations with solutions associated to Fibonacci numbers, Electron. J. Math. Analysis. Appl. 5 (2017), 166–178.10.21608/ejmaa.2017.310883Search in Google Scholar

[17] Halim, Y.—Rabago, J. F. T.: On the solutions of a second-order difference equations in terms of generalized Padovan sequences, Math. Slovaca 68 (2018), 625–638.10.1515/ms-2017-0130Search in Google Scholar

[18] Halim, Y.—Khelifa, A.—Mokrani, N.: Connection of Balancing numbers with solutions of a system of two higher-order difference equations, Miskolc Math. Notes 24 (2023), 779–788.10.18514/MMN.2023.4315Search in Google Scholar

[19] Halim, Y.—Khelifa, A.—Berkal, M.—Bouchair, A.: On a solvable system of p difference equations of higher order, Period. Math. Hungar. 85 (2022), 109–127.10.1007/s10998-021-00421-xSearch in Google Scholar

[20] Halim, Y.—Berkal, M.—Khelifa, A.: On a three-dimensional solvable system of difference equations, Turk. J. Math. 44(2) (2020), 1263–1288.10.3906/mat-2001-40Search in Google Scholar

[21] Khelifa, A.—Halim, Y.—Berkal, M.: On the solutions of a system of (2p+1) difference equations of higher order, Miskolc Math. Notes 22(2) (2021), 331—350.10.18514/MMN.2021.3385Search in Google Scholar

[22] Khelifa, A.—Halim, Y.—Berkal, M.: Solutions of a system of two higher-order difference equations in terms of Lucas sequence, Univers. J. Math. Appl. 2(4) (2019), 202—211.10.32323/ujma.610399Search in Google Scholar

[23] Khelifa, A.—Halim, Y.—Bouchair, A.—Berkal, M.: On a system of three difference equations of higher order solved in terms of Lucas and Fibonacci numbers, Math. Slovaca 70(3) (2021), 641–656.10.1515/ms-2017-0378Search in Google Scholar

[24] Khelifa, A.—Halim, Y.: General solutions to systems of difference equations and some of their representations, J. Appl. Math. Comput. 67 (2021), 439–453.10.1007/s12190-020-01476-8Search in Google Scholar

[25] Panda, G. K.: Sequence balancing and cobalancing numbers, Fibonacci Quart. 45 (2007), 265–271.10.1080/00150517.2007.12428219Search in Google Scholar

[26] Panda, G. K.—Ray, P. K.: Cobalancing numbers and cobalancers, Int. J. Math. Math. Sci. 8 (2005), 1189–1200.10.1155/IJMMS.2005.1189Search in Google Scholar

[27] Tollu, D. T.—Yazlik, Y.—Taskara, Y.: On fourteen solvable systems of difference equations Appl. Math. Comput. 233(1) (2014), 310–319.10.1016/j.amc.2014.02.001Search in Google Scholar

[28] Tollu, D. T.—Yazlik, Y.—Taskara, Y.: On the solutions of two special types of Riccati difference equation via Fibonacci numbers, Adv. Difference Equ. 174 (2013), 1–7.10.1186/1687-1847-2013-174Search in Google Scholar

[29] Touafek, N.: On some fractional systems of difference, Iran. J. Math. Sci. Inform. 9(2) (2014), 303–305.Search in Google Scholar

[30] Touafek, N.: On a second order rational difference equation, Hacet. J. Math. Stat. 41(6) (2012), 867–874.Search in Google Scholar

[31] Touafek, N.: On a general system of difference equations defined by homogeneous functions, Math. Slovaca 71(3) (2021), 697–720.10.1515/ms-2021-0014Search in Google Scholar

[32] Yazlik, Y.—Tollu, D. T.—Taskara, N.: Behaviour of solutions for a system of two higher-order difference equations, J. Sci. Arts 45(4) (2018), 813–826.Search in Google Scholar

[33] Yazlik, Y.—Kara, M.: On a solvable system of difference equations of higher-order with period two coefficients Commun. Fac. Sci. Univ. Ank. Sr. A1 Math. Stat. 68(2) (2019), 1675–1693.10.31801/cfsuasmas.548262Search in Google Scholar