Dergiler / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2021 / Cilt: 70 - Sayı: 2

Fractional variational problems on conformable calculus

Sayfa
719–730
Yayın Tarihi
2021-12-31
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Then, we studied on the variational problems with integral constraints and holonomic constraints, respectively.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:In this paper, we deal with the variational problems defined by an integral that include fractional conformable derivative.
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Temel Bulgular & Veri:We obtained the optimality results for variational problems with fixed end-point boundary conditions and variable end-point boundary conditions.
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Sonuç & Katkı:Then, we studied on the variational problems with integral constraints and holonomic constraints, respectively.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Conformable fractional derivative · calculus of variations · subsidiary conditions

Abstract

In this paper, we deal with the variational problems defined by an integral that include fractional conformable derivative. We obtained the optimality results for variational problems with fixed end-point boundary conditions and variable end-point boundary conditions. Then, we studied on the variational problems with integral constraints and holonomic constraints, respectively.

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Bu Makaleye Atıf Yap

ÖĞREKÇİ, S., ASLIYÜCE, S. (2021). Fractional variational problems on conformable calculus. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Cilt: 70 - Sayı: 2, 719–730. https://ajindex.com/articles/746696

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Kaynakça (14)

  1. Abdeljawad, T., On conformable fractional calculus. J. Comput. Appl. Math., 279 (2015), 57-66. https://doi.org/10.1016/j.cam.2014.10.016
  2. Agarwal, O. P., Formulation of Euler-Lagrange equations for fractional variational problems. J. Math. Anal. Appl., 272 (2002), 368-379. https://doi.org/10.1016/S0022-247X(02)00180-4
  3. Agarwal, O. P., Fractional variational calculus and the transversality conditions. J. Phys. A, 39 (33) (2006), 10375-10384. https://doi.org/10.1088/0305-4470/39/33/008
  4. Agarwal, O. P., Fractional variational calculus in terms of Riesz fractional derivatives. J. Phys. A, 40 (24) (2007), 6287-6303. https://doi.org/10.1088/1751-8113/40/24/003
  5. Almeida, R., Fractional variational problems with the Riesz-Caputo derivative. Appl. Math. Lett., 25 (2) (2012), 142-148. https://doi.org/10.1016/j.aml.2011.08.003
  6. Almeida, R., Variational problems involving a Caputo-type fractional derivative. J. Optim. Theory Appl., 174 (1) (2017), 276-294. https://doi.org/10.1007/s10957-016-0883-4
  7. Bastos, N. R. O., Calculus of variations involving Caputo-Fabrizio fractional differentiation. Stat., Optim. Inf. Comput., 6 (2018), 12-21. https://doi.org/10.19139/soic.v6i1.466
  8. Batarfi, H., Losada, J., Nieto, J. J., Shammakh, W., Three-point boundary value problems for conformable fractional differential equations. J. Funct. Spaces, 2015, Art. ID 706383, 6 pp. https://doi.org/10.1155/2015/706383
  9. Chatibi, Y., El Kinani, E. H., Ouhadan, A., Lie symmetry analysis of conformable differential equations. AIMS Math., 4 (4) (2019), 1133--1144. https://doi.org/10.3934/math.2019.4.1133
  10. Chatibi, Y., El Kinani, E. H., and Ouhadan, A., Variational calculus involving nonlocal fractional derivative with Mittag-Leffler kernel. Chaos, Solitons & Fractals, 118 (2019), 117-121. https://doi.org/10.1016/j.chaos.2018.11.017
  11. Chatibi, Y., El Kinani, E. H., Ouhadan, A., Lie symmetry analysis and conservation laws for the time fractional Black-Scholes equation. International Journal of Geometric Methods in Modern Physics, 17 (01) (2020), 2050010. https://doi.org/10.1142/S0219887820500103
  12. Chatibi, Y., El Kinani, E. H., Ouhadan, A., On the discrete symmetry analysis of some classical and fractional differential equations. Math. Methods Appl. Sci., 44 (4) (2021), 2868--2878. https://doi.org/10.1002/mma.6064
  13. Chung, W. S., Fractional Newton mechanics with conformable fractional derivative. J. Comput. Appl. Math., 290 (2015), 150-158. https://doi.org/10.1016/j.cam.2015.04.049
  14. Çenesiz, Y., Kurt, A., The soluti