PL EN


Preferences help
enabled [disable] Abstract
Number of results
2017 | 132 | 3 | 658-662
Article title

Optimal Control Problem for a Conformable Fractional Heat Conduction Equation

Content
Title variants
Languages of publication
EN
Abstracts
EN
This paper presents an optimal boundary temperature control of thermal stresses in a plate, based on time-conformable fractional heat conduction equation. The aim is to find the boundary temperature that takes thermal stress under control. The fractional Laplace and finite Fourier sine transforms are used to obtain the fundamental solution. Then the optimal control is held by successive iterations. Numerical results are depicted by plots produced by MATLAB codes.
Keywords
Contributors
  • Balıkesir University, Faculty of Science and Arts, Department of Mathematics, Balıkesir, Turkey
author
  • Balıkesir University, Faculty of Science and Arts, Department of Mathematics, Balıkesir, Turkey
author
  • Balıkesir University, Faculty of Science and Arts, Department of Mathematics, Balıkesir, Turkey
References
  • [1] Y.Z. Povstenko, Fractional Thermoelasticity, Springer, Switzerland 2015
  • [2] I. Podlubny, Fractional Differential Equations, Academic Press, New York 1999
  • [3] Y.Z. Povstenko, J. Therm. Stress. 28, 83 (2004), doi: 10.1080/014957390523741
  • [4] Y.Z. Povstenko, Quart. J. Mechan. Appl. Math. 61, 523 (2008), doi: 10.1093/qjmam/hbn016
  • [5] Y.Z. Povstenko, Mechan. Res. Communicat. 37, 436 (2010), doi: 10.1016/j.mechrescom.2010.04.006
  • [6] Y.Z. Povstenko, Phys. Scripta T136, 014017 (2009), doi: 10.1088/0031-8949/2009/T136/014017
  • [7] N. Ozdemir, Y. Povstenko, D. Avci, B.B. Iskender, J. Therm. Stress. 37, 969 (2014), doi: 10.1080/01495739.2014.912937
  • [8] F. Knopp, Time-optimal boundary condition against thermal stress, in: 9th Int. Congr. Thermal Stresses, Budapest, Hungary 2011
  • [9] R. Khalil, M. Al Horani, A. Yousef, M. Sababheh, J. Computat. Appl. Math. 264, 65 (2014), doi: 10.1016/j.cam.2014.01.002
  • [10] T. Abdeljawad, J. Computat. Appl. Math. 279, 57 (2015), doi: 10.1016/j.cam.2014.10.016
  • [11] Y. Cenesiz, A. Kurt, Acta Univ. Sapient. Math. 7, 130 (2015), doi: 10.1515/ausm-2015-0009
  • [12] Y. Cenesiz, A. Kurt, in: Proc. 8th Int. Conf. Applied Mathematics, Simulation, Modelling (ASM'14) Florence, Italy 2014, p. 195
  • [13] M. Abu Hammad, R. Khalil, Int. J. Pure Appl. Math. 94, 215 (2014), doi: 10.12732/ijpam.v94i2.8
  • [14] A.A. Kilbas, H.M. Srivastava, J.J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam 2006
  • [15] D. Baleanu, T. Blaszcyk, J. Asad, M. Alipour, Acta Phys. Pol. A 130, 688 (2016), doi: 10.12693/APhysPolA.130.688
  • [16] A. Atangana, Derivative with a New Parameter: Theory, Methods and Applications, Academic Press, 2015
  • [17] X.J. Yang, D. Baleanu, H.M. Srivastava, Local Fractional Integral Transforms and Their Applications, Academic Press, 2015
  • [18] A. Atangana, D. Baleanu, Therm. Sci. 20, 763 (2016), doi: 10.2298/TSCI160111018A
  • [19] R. Almeida, M. Guzowska, T. Odzijewicz, Open Math. 14, 1122 (2016), doi: 10.1515/math-2016-0104
  • [20] V.E. Tarasov, Intern. J. Appl. Computat. Math. 2, 195 (2016), doi: 10.1007/s40819-015-0054-6
  • [21] A. Atangana, D. Baleanu, A. Alsaedi, Open Math. 13, 889 (2015), doi: 10.1515/math-2015-0081
  • [22] B. Nagy, Acta Phys. Pol. A 128, B-164 (2015), doi: 10.12693/APhysPolA.128.B-164
  • [23] A. Kudaykulov, A. Zhumadillayeva, Acta Phys. Pol. A 130, 335 (2016), doi: 10.12693/APhysPolA.130.335
  • [24] Z. Akhmetova, S. Zhuzbaev, S. Boranbayev, Acta Phys. Pol. A 130, 352 (2016), doi: 10.12693/APhysPolA.130.352
Document Type
Publication order reference
Identifiers
YADDA identifier
bwmeta1.element.bwnjournal-article-appv132n3p068kz
JavaScript is turned off in your web browser. Turn it on to take full advantage of this site, then refresh the page.