TY - JOUR T1 - A Note on Hyper-Dual Numbers with the Leonardo-Alwyn Sequence AU - Saçlı, Gülsüm Yeliz AU - Yüce, Salim PY - 2024 DA - June DO - 10.47000/tjmcs.1344439 JF - Turkish Journal of Mathematics and Computer Science JO - TJMCS PB - Matematikçiler Derneği WT - DergiPark SN - 2148-1830 SP - 154 EP - 161 VL - 16 IS - 1 LA - en AB - We are interested in identifying hyper-dual numbers with the Leonardo-Alwyn sequence components. We investigate their homogeneous and non-homogeneous recurrence relations, the Binet’s formula, and the generating function. With these algebraic properties, we are able to obtain some special cases of hyper-dual numbers with the Leonardo-Alwyn sequence according to $p,q$ and $c$ (multipliers). KW - Leonardo sequence KW - Recurrence relation KW - Hyper-dual number CR - Alp, Y., Koçer, E.G., Hybrid Leonardo numbers, Chaos, Solitons & Fractals, 150(2021). CR - Alp, Y., Koçer, E.G., Some properties of Leonardo numbers, Konuralp Journal of Mathematics, 9(1)(2021), 183–189. CR - Catarino, P., Borges, A., On Leonardo numbers, Acta Math. Univ. Comenianae, 89(1) (2020), 75–86. CR - Cohen, A., Shoham, M., Principle of transference-An extension to hyper-dual numbers, Mech. Mach. Theory, 125(2018), 101–110. CR - Fike, J.A., Alonso, J.J., Automatic differentiation through the use of hyper-dual numbers for second derivatives, Lecture Notes in ComputationalScience and Engineering book series (LNCSE), 87(2011), 163–173. CR - Gökbaş, H. A new family of number sequences: Leonardo-Alwyn numbers, Armenian Journal of Mathematics, 15(6)(2023), 1–13. CR - Horadam, A. F., Generating functions for powers of a certain generalised sequence of numbers, Duke Mathematical Journal, 32(3)(1965), 437–446. CR - Horadam, A.F. Basic properties of a certain generalized sequence of numbers, The Fibonacci Quarterly, 3(3)(1965), 161–176. CR - Horadam, A.F. Special properties of the sequence Wn(a, b; p, q), The Fibonacci Quarterly, 5(5)(1967), 424–434. CR - Kantor, I., Solodovnikov, A., Hypercomplex Numbers. Springer-Verlag, New York, 1989. CR - Karatas, A., On complex Leonardo numbers, Notes on Number Theory and Discrete Mathematics, 28(3)(2022), 458–465. CR - Karakuş, S.Ö ., Nurkan, S.K., Turan, M., Hyper-dual Leonardo numbers, Konuralp Journal of Mathematics, 10(2)(2022), 269–275. CR - Koshy, T., Fibonacci and Lucas Numbers with Applications, John Wiley & Sons, New York, 2001. CR - Kuhapatanakul, K., Chobsorn, J. On the generalized Leonardo numbers, Integers, 22 (2022). CR - Nurkan, S.K., Güven, İ.A., Ordered Leonardo quadruple numbers, Symmetry, 15(1)(2023), 149. CR - Özimamoğlu, H., A new generalization of Leonardo hybrid numbers with q-integers, Indian Journal of Pure and Applied Mathematics, (2023). CR - Pennestr`ı, E., Stefanelli, R., Linear algebra and numerical algorithms using dual numbers, Multibody Syst. Dyn., 18(2007), 323–344. CR - Shannon, A.G., Deveci, O¨ ., A note on generalized and extended Leonardo sequences, Notes on Number Theory and Discrete Mathematics, 28(1)(2022), 109–114. CR - Soykan, Y. Special cases of generalized Leonardo numbers: modified p-Leonardo, p-Leonardo-Lucas and p-Leonardo Numbers, Earthline Journal of Mathematical Sciences, 11(2)(2023), 317–342. CR - Study, E., Geometrie der dynamen: Die Zusammensetzung von Kr¨aften und Verwandte Gegenst¨ande der Geometrie Bearb., Leipzig, B.G. Teubner. 1903. CR - Tan, E., Leung, H.H., On Leonardo p-numbers, Integers, 23(2023). CR - Yaglom, I.M., A Simple Non-Euclidean Geometry and Its Physical Basis, Springer-Verlag, New York, 1979. CR - Yilmaz, Ç.Z., Saçlı, G.Y., On dual quaternions with k- generalized Leonardo components, Journal of New Theory, 44(2023), 31–42. UR - https://doi.org/10.47000/tjmcs.1344439 L1 - https://dergipark.org.tr/en/download/article-file/3337970 ER -