THE EXACT SOLUTIONS OF SOME DIFFERENCE EQUATIONS ASSOCIATED WITH ADJUSTED JACOBSTHAL-PADOVAN NUMBERS

Yıl 2022, Cilt: 8 Sayı: 1, 1 - 14, 30.06.2022

Melih Göcen

https://doi.org/10.34186/klujes.1078836

Öz

In this paper, we obtain the form of the solutions of some rational difference equations via adjusted Jacobsthal-Padovan numbers. We find a relation between the exact solutions and the adjusted Jacobsthal-Padovan numbers. Apart from the literature, we give the closed form of the solutions associated with these well-known integer sequence using exponential functions. Furthermore, we investigate the asymptotic behavior of the equilibrium point of the solutions of these difference equations.

Anahtar Kelimeler

Difference equation, Form of the solutions, Stability, Jacobsthal-Padovan numbers

BAZI FARK DENKLEMLERİNİN AYARLANMIŞ JACOBSTHAL-PADOVAN SAYILARI İLE İLİŞKİLİ TAM ÇÖZÜMLERİ

Öz

Bu makalede, bazı rasyonel fark denklemlerinin ayarlanmış Jacobsthal-Padovan sayıları ile çözümlerinin formunu elde ediyoruz. Kesin çözümler ile ayarlanmış Jacobsthal-Padovan sayıları arasında bir ilişki buluyoruz. Literatürün dışında, çözümlerin bu iyi bilinen diziler ile ilişkili kapalı formunu üstel fonksiyonlar kullanarak veriyoruz. Ayrıca, bu fark denklemlerinin denge noktasının asimptotik davranışını inceliyoruz.

Anahtar Kelimeler

Fark denklemi, Çözümlerin formu, Karalılık, Jacobsthal-Padovan sayıları.

Kaynakça

• Referans1 Deveci, Ö., The Pell-Padovan sequences and the Jacobsthal-Padovan sequences in finite groups, Util. Math., 98, 257-270, 2015.
• Referans2 Deveci, Ö., The Jacobsthal-Padovan p-sequences and their applications, Proc. Rom. Acad. Ser. A, 20(3), 215-224, 2019.
• Referans3 Göcen, M., Cebeci, A., On the perodie solutions of some systems of higher order difference equation, Rocky Mt. J. Math., 48(3), 845-858, 2018.
• Referans4 Göcen, M., Güneysu, M., The global attractivity of some rational difference equations, J. Comput. Anal. Appl., 25(7), 1233-1243, 2018.
• Referans5 Haddad N., Tonafek, N., Rabago, J. F. T., Solution form of a higher-oreder system of difference equations and dynamical behavior of its special case, Math. Methods Appl. Sci., 40(10), 3599-3607, 2017.
• Referans6 Halim, Y., Bayram, M., On the solutions of a higher-order difference equation in terms of generalized Fibonacci sequences. Mathematical Methods in the Applied Seciences, 39, 2974-2982, 2016.
• Referans7 Halim, Y., A System of Difference Equations with Solutions Associated to Fibonacci Numbers. International Journal of Difference Equations, 11(1), 65-77, 2016.
• Referans8 Halim, Y., Rabago, J. F. T., On the Some Solvable Systems of Difference Equations with Solutions Associated to Fibonacci numbers. Electronic Journal of Mathematical Analysis and Applications, 5(1), 166-178, 2017.
• Referans9 Halim, Y., On the Solutions of a Second-Order Difference Equation in terms of Generalized Padovan Sequences. Mathematica Slovaca, 68(3), 625-638, 2018.
• Referans10 Okumuş, İ., Soykan, Y., On the Solutions of Four Rational Defference Equations Associated to Tribonacci Numbers, preprints.org, doi. 10.20944/preprints201906.0266.v1., 2019.
• Referans11 Kara, M., Yazlik, Y., On a Solvabe Three-Dimensional System of Difference Equations, Filomat, 34(4), 1167-1186, 2020.
• Referans12 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), 641-656, 2020.
• Referans13 Khelifa, A., Halim Y., General solutions to system of difference equations and some of their representations. J. Appl. Math. Comput., 67(3), 439-453, 2021.
• Referans14 Kulenovic M. R. S., Ladas, G., Dynamic of second order rational difference equations: With Open Problems and Conjectures, Chapman Hall/ CRC, Boca Raton, FL, 2002.
• Referans15 R. Abo-Zeid, Behavior of solutions of a second order rational difference equation, Math. Morav., 23, 11-25, 2019.
• Referans16 N. J. A. Sloane, The on-line encyclopedia of integer sequences, http://oeis.org/.
• Referans17 Soykan, Y., A Study on Generalized Jacobsthal-Padovan Numbers, Earthline Journal of Mathematical Seciences, 4(2), 227-251, 2020.
• Referans18 Soykan, Y., A Study On Generalized (r; s; t)- Numbers. MathLAB Journal, 7, 101-129, 2020.
• Referans19 Taşdemir, E. Global dynamics of a higher order difference equation with a quadratic term. J. Appl. Math. Comput., 67(1-2), 423-437, 2021.
• Referans20 Yacine, H., Form and periodicity of solutions of some system of higherorder difference equation, Math. Sci. Lett., 5(1), 79-84, 2016.
• Referans21 Yazlik, Y., Tollu, D. T., Taskara, N., On the Solutions of Difference Equation System With Padovan Numbers. Applied Mathematics, 4, 15-20. 2013.