On a solvable difference equations system of second order its solutions are related to a generalized Mersenne sequence
-
Murad Khan Hassani
and
Yasin Yazlik
Abstract
In this paper, we consider a class of two-dimensional nonlinear difference equations system of second order, which is a considerably extension of some recent results in the literature. Our main results show that class of system of difference equations is solvable in closed form theoretically. It is noteworthy that the solutions of aforementioned system are associated with generalized Mersenne numbers. The asymptotic behavior of solution to aforementioned system of difference equations when a = b and p = 0 are also given. Finally, numerical examples are given to support the theoretical results presented in this paper.
Acknowledgement
The authors thanks the referees for his (her) comments and suggestions.
Communicated by Michal Fečkan
References
[1] Abo-Zeid, R.: On the solutions of a higher order difference equation, Georgian Math. J. 27(2) (2020), 165–175.10.1515/gmj-2018-0008Search in Google Scholar
[2] Abo-Zeid, R.: Behavior of solutions of a second order rational difference equation, Math. Moravica 23(1) (2019), 11–25.10.5937/MatMor1901011ASearch in Google Scholar
[3] Din, Q.: Asymptotic behavior of an anti-competitive system of second-order difference equations, J. Egypt. Math. Soc. 24 (2016), 37–43.10.1016/j.joems.2014.08.008Search in Google Scholar
[4] Elabbasy, E. M.—El-Metwally, H.—Elsayed, E. M.: Qualititive behavior of higher order difference equations, Soochow J. Math. 33 (2007), 861–873.Search in Google Scholar
[5] Elsayed, E. M.—Alzahrani, F.—Abbas, I.—Alotaibi N. H.: Dynamical behavior and solution of nonlinear difference equation via Fibonacci sequence, J. Appl. Anal. Comput. 10(1) (2020), 282–296.10.11948/20190143Search in Google Scholar
[6] Elsayed, E. M.: On the solutions and periodic nature of some systems of difference equations, Int. J. Biomath. 7(6) (2014), Art. ID 1450067.10.1142/S1793524514500673Search in Google Scholar
[7] Halim, Y.—Bayram, M.: On the solutions of a higher-order difference equation in terms of generalized Fibonacci sequences, Math. Methods Appl. Sci. 39(11) (2016), 2974–2982.10.1002/mma.3745Search in Google Scholar
[8] Halim, Y.—Rabago, J. F. T.: On the solutions of a second-order difference equation in terms of generalized Padovan sequences, Math. Slovaca 68(3) (2018), 625–638.10.1515/ms-2017-0130Search in Google Scholar
[9] Haddad, N.—Touafek, N.—Rabago, J. F. T.: Well-defined solutions of a system of difference equations, J. Appl. Math. Comput., 56(1-2) (2018), 439–458.10.1007/s12190-017-1081-8Search in Google Scholar
[10] Kara, M.—Yazlik, Y.: On eight solvable systems of difference equations in terms of generalized Padovan sequences, Miskolc Math. Notes 22(2) (2021), 695–708.10.18514/MMN.2021.3234Search in Google Scholar
[11] Kara, M.—Yazlik, Y.: Solvability of a system of non-linear difference equations of higher order, Turk. J. Math., 43(3) (2019), 1533–1565.10.3906/mat-1902-24Search in Google Scholar
[12] Khelifa, A.—Hhalim, 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) (2020), 641–656.10.1515/ms-2017-0378Search in Google Scholar
[13] Stević, S.: On a solvable system of difference equations of k-th order, Appl. Math. Comput., 219 (2013), 7765–7771.10.1016/j.amc.2013.01.064Search in Google Scholar
[14] Tollu, D. T.—Yazlik, Y.—Taskara, N.: On the solutions of two special types of Riccati difference equation via Fibonacci numbers, Adv. Difference Equ. 2013 (2013), Art. 174.10.1186/1687-1847-2013-174Search in Google Scholar
[15] Tollu, D. T.—Yazlik, Y.—Taskara, N.: On fourteen solvable systems of difference equations, Appl. Math. Comput. 233 (2014), 310–319.10.1016/j.amc.2014.02.001Search in Google Scholar
[16] Touafek, N.—Elsayed, E. M.: On the periodicity of some systems of nonlinear difference equations, Bull. Math. Soc. Sci. Math. Roum. Nouv. Sér. 55(103) (2012), 217–224.Search in Google Scholar
[17] Touafek, N.—Elsayed, E. M.: On a second order rational systems of difference equations, Hokkaido Math. J. 44 (2015), 29–45.10.14492/hokmj/1470052352Search in Google Scholar
[18] Yazlik, Y.—Kara, M.: On a solvable system of difference equations of higher-order with period two coefficients, Commun. Fac. Sci. Univ. Ank., Sér. A1, Math. Stat. 682(2) (2019), 1675–1693.10.31801/cfsuasmas.548262Search in Google Scholar
© 2024 Mathematical Institute Slovak Academy of Sciences
Articles in the same Issue
- On the Paley graph of a quadratic character
- A topological duality for tense modal pseudocomplemented De Morgan algebras
- Fibonacci numbers as mixed concatenations of Fibonacci and Lucas numbers
- A general formula in composition theory
- A nonlinear Filbert-like matrix with three free parameters: From linearity to nonlinearity
- On universality in short intervals for zeta-functions of certain cusp forms
- On asymptotics for lacunary partition functions
- Parallel surfaces of the non-lightlike solution of vortex filament equations
- New q-analogues of Van Hamme’s (F.2) supercongruence and of some related supercongruences
- Kneser-type oscillation theorems for second-order functional differential equations with unbounded neutral coefficients
- Approximation theorems via Pp-statistical convergence on weighted spaces
- Global existence and multiplicity of positive solutions for anisotropic eigenvalue problems
- Theoretical analysis of higher-order system of difference equations with generalized balancing numbers
- On a solvable difference equations system of second order its solutions are related to a generalized Mersenne sequence
- Positive bases, cones, Helly-type theorems
- Digital Jordan surfaces arising from tetrahedral tiling
- Influence of ideals in compactifications
- On the functions ωf and Ωf
- On the 𝓐-generators of the polynomial algebra as a module over the Steenrod algebra, I
- A bivariate distribution with generalized exponential conditionals
- A note on boundary feedback stabilization for degenerate parabolic equations in multi-dimensional domains
Articles in the same Issue
- On the Paley graph of a quadratic character
- A topological duality for tense modal pseudocomplemented De Morgan algebras
- Fibonacci numbers as mixed concatenations of Fibonacci and Lucas numbers
- A general formula in composition theory
- A nonlinear Filbert-like matrix with three free parameters: From linearity to nonlinearity
- On universality in short intervals for zeta-functions of certain cusp forms
- On asymptotics for lacunary partition functions
- Parallel surfaces of the non-lightlike solution of vortex filament equations
- New q-analogues of Van Hamme’s (F.2) supercongruence and of some related supercongruences
- Kneser-type oscillation theorems for second-order functional differential equations with unbounded neutral coefficients
- Approximation theorems via Pp-statistical convergence on weighted spaces
- Global existence and multiplicity of positive solutions for anisotropic eigenvalue problems
- Theoretical analysis of higher-order system of difference equations with generalized balancing numbers
- On a solvable difference equations system of second order its solutions are related to a generalized Mersenne sequence
- Positive bases, cones, Helly-type theorems
- Digital Jordan surfaces arising from tetrahedral tiling
- Influence of ideals in compactifications
- On the functions ωf and Ωf
- On the 𝓐-generators of the polynomial algebra as a module over the Steenrod algebra, I
- A bivariate distribution with generalized exponential conditionals
- A note on boundary feedback stabilization for degenerate parabolic equations in multi-dimensional domains
