KaydedilenlerDerginizi ekleyin

Dergiler / Hacettepe Journal of Mathematics and Statistics / 2020 / Cilt: 49 - Sayı: 1

Calculus of variations on time scales with nabladerivatives of exponential function

Jie BAİ
Ling Bai
Zhijun Zeng
Sayfa
68–77
Yayın Tarihi
2022-10-18
DOI
—
🏛️Bu makalenin bibliyografik verileri ve tam metin bağlantısı DergiPark üzerinden sağlanmıştır.
DergiPark Kaydı ↗
✨

Yapay Zeka Hızlı Bakış & Çıkarımlar

AI Insight
⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

As applications of these results, an exampleof conditional extremum is provided.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:In this paper, we study the calculus of variations of the nabla notion on time scalesincluding∇-derivative,∇-integral, and∇-derivatives of exponential function.
📊
Temel Bulgular & Veri:The Euler-Lagrange equations of the first-order both single-variable problem and multivariable prob-lem with nabla derivatives of exponential function on time scales are obtained.
💡
Sonuç & Katkı:As applications of these results, an exampleof conditional extremum is provided.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Alan Parametreleri

Abstract

In this paper, we study the calculus of variations of the nabla notion on time scalesincluding∇-derivative,∇-integral, and∇-derivatives of exponential function. The Euler-Lagrange equations of the first-order both single-variable problem and multivariable prob-lem with nabla derivatives of exponential function on time scales are obtained. In par-ticular, we show that the calculus of variations with multiple variables could solve theproblem of conditional extreme value. Moreover, we verify the solution to the multivari-able problem is exactly the extremum pair. As applications of these results, an exampleof conditional extremum is provided.

🔖

Bu Makaleye Atıf Yap

BAİ, J., Bai, L., Zeng, Z. (2022). Calculus of variations on time scales with nabladerivatives of exponential function. Hacettepe Journal of Mathematics and Statistics, Cilt: 49 - Sayı: 1, 68–77. https://ajindex.com/articles/529692

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (1)

  1. R. Agarwal, M. Bohner, D. O’Regan and A. Peterson,Dynamic equations on timescales: a survey, J. Comput. Appl. Math.141(1), 1–26, 2002. [2]C.D. Ahlbrandt, M. Bohner and J. Ridenhour,Hamiltonian systems on time scales,J. Math. Anal. Appl.250(2), 561–578, 2000. [3]R. Almeida and D.F. Torres,Isoperimetric problems on time scales with nabla deriva-tives,J. Vib. Control,15(6), 951–958, 2009. [4]F.M. Atici, D.C. Biles and A. Lebedinsky,An application of time scales to economics,Math. Comput. Model.43(7-8), 718–726, 2006. [5]Z. Bartosiewicz and E. Pawluszewicz,Realizations of nonlinear control systems ontime scales, IEEE Trans. Autom. Control,53(2), 571–575, 2008. [6]Z. Bartosiewicz and E. Pawluszewicz,Dynamic feedback equivalence of time-variantcontrol systems on homogeneous time scales, Int. J. Math. Stat.5(A09), 11–20, 2009. [7]Z. Bartosiewicz, N. Martins and D.F. Torres,The second euler-lagrange equation ofvariational calculus on time scales, Eur. J. Control,17(1), 9–18, 2011. [8]Z. Bartosiewicz, E. Piotrowska and M. Wyrwas,Stability, stabilization and observersof linear control systems on time scales, Proc. IEEE Conf. on Decision and Control,New Orleans, LA, USA, 2803–2808, 2007. [9]Z. Bartosiewicz, U. Kotta, E. Pawluszewicz and M. Wyrwas,Algebraic formalism ofdiffer- ential one-forms for nonlinear control systems on time scales, Proc. Est. Acad.Sci.56(3), 264–282, 2007. [10]M. Bohner,Calculus of variations on time scales, Dynam. Syst. Appl.13(3-4), 339–349, 2004. [11]M. Bohner and A. Peterson,Dynamic equations on time scales: An introduction withapplications, Birkhauser Boston, Boston, MA, 2001 [12]J.J. DaCunha,Stability for time varying linear dynamic systems on time scales, J.Comput. Appl. Math.176(2), 381–410, 2005. [13]R. David,Advanced macroeconomics, McGraw-Hill, Irwin, 2011. [14]R.A. Ferreira and D.F. Torres,Remarks on the calculus of variations on time scales,Int. J. Ecol. Econ. Stat.9(F07), 65–73, 2007. [15]R.A. Ferreira and D.F. Torres,Higher-order calculus of variations on time scales, in:Mathematical Control Theory and Finance, Springer, Berlin,136(1), 149–159, 2008. [16]M. Guzowska, A.B. Malinowska and M.R.S. Ammi,Calculus of variations on timescales: applications to economic models, Adv. Differ. Equ.2015(1), 203, 2015. [17]R. Hilscher and V. Zeidan,Calculus of variations on time scales: weak local piecewisecrd1 solutions with variable endpoints, J. Math. Anal. Appl.289(1), 143–166, 2004. [18]R. Hilscher and V. Zeidan,Weak maximum principle a