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New features of the fractional Euler-Lagrange equations for a physical system within non-singular derivative operator

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Abstract.

Free motion of a fractional capacitor microphone is investigated in this paper. First, a capacitor microphone is introduced and the Euler-Lagrange equations are established. Due to the fractional derivative's the history independence, the fractional order displacement and electrical charge are used in the equations. Fractional differential equations involve in the right- and left-hand-sided derivatives which is reduced to a boundary value problem. Finally, numerical simulations are obtained and dynamical behaviors are numerically discussed.

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References

  1. W. Greiner, Classical Mechanics, Systems of Particles and Hamiltonian Dynamics (Springer-Verlag, Berlin Heidelberg, 2010)

  2. R. Gorenflo, F. Mainardi, Fractional calculus: Integral and Differential Equations of Fractional Orders, Fractals and Fractional Calculus in Continoum Mechanics (Springer-Verlag, Wien and New York, 1997)

  3. R. Hilfer, Applications of Fraction Calculus in Physics (World Scientific, Singapore, 2000)

  4. D. Baleanu, J.A.T. Machado, A.C.J. Luo, Fractional Dynamics and Control (Springer-Verlag, New York, 2012)

  5. A. Jajarmi, M. Hajipour, E. Mohammadzadeh, D. Baleanu, J. Franklin Inst. 335, 3938 (2018)

    Article  Google Scholar 

  6. A. Jajarmi, D. Baleanu, J. Vib. Control 24, 2430 (2018)

    Article  MathSciNet  Google Scholar 

  7. A. Jajarmi, D. Baleanu, Chaos, Soliton. Fractals 113, 221 (2018)

    Article  ADS  Google Scholar 

  8. D. Baleanu, A. Jajarmi, E. Bonyah, M. Hajipour, Adv. Differ. Equ. 2018, 230 (2018)

    Article  Google Scholar 

  9. D. Kumar, J. Singh, D. Baleanu, Eur. Phys. J. Plus 133, 70 (2018)

    Article  Google Scholar 

  10. F. Tchier, M. Inc, A. Yusuf, A.I. Aliyu, D. Baleanu, Eur. Phys. J. Plus 133, 240 (2018)

    Article  Google Scholar 

  11. D. Kumar, J. Singh, D. Baleanu, S. Rathore, Eur. Phys. J. Plus 133, 259 (2018)

    Article  Google Scholar 

  12. M. Hajipour, A. Jajarmi, D. Baleanu, H.G. Sun, Commun. Nonlinear Sci. 69, 119 (2019)

    Article  Google Scholar 

  13. F. Riewe, Phys. Rev. E 53, 1890 (1996)

    Article  ADS  MathSciNet  Google Scholar 

  14. F. Riewe, Phys. Rev. E 55, 3581 (1997)

    Article  ADS  MathSciNet  Google Scholar 

  15. N. Laskin, Phys. Rev. E 62, 3135 (2000)

    Article  ADS  Google Scholar 

  16. N. Laskin, Phys. Lett. A 268, 298 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  17. N. Laskin, Phys. Rev. E 66, 056108 (2002)

    Article  ADS  MathSciNet  Google Scholar 

  18. D. Baleanu, S. Muslih, Phys. Scr. 72, 119 (2005)

    Article  ADS  Google Scholar 

  19. D. Baleanu, A. Jajarmi, J.H. Asad, T. Blaszczyk, Acta Phys. Pol. A 131, 1561 (2017)

    Article  Google Scholar 

  20. D. Baleanu, J.H. Asad, A. Jajarmi, Proc. Rom. Acad. A 19, 361 (2018)

    Google Scholar 

  21. D. Baleanu, J.H. Asad, A. Jajarmi, Proc. Rom. Acad. A 19, 447 (2018)

    Google Scholar 

  22. A.A. Kilbas, H.M. Srivastava, J.J. Trujillo, Theory and Applications of Fractional Differential Equations (Elsevier, Amsterdam, 2006)

  23. D. Baleanu, J.H. Asad, I. Petras, Rom. Rep. Phys. 64, 907 (2012)

    Google Scholar 

  24. D. Baleanu, J.H. Asad, I. Petras, Commun. Theor. Phys. 61, 221 (2014)

    Article  Google Scholar 

  25. S. Momani, Z. Odibat, Numer. Methods Part. Differ. Equ. 24, 1416 (2008)

    Article  Google Scholar 

  26. K. Diethelm, N.J. Ford, A.D. Freed, Nonlinear Dyn. 29, 3 (2002)

    Article  Google Scholar 

  27. A. Atangana, D. Baleanu, Therm. Sci. 20, 763 (2016)

    Article  Google Scholar 

  28. H. Srivastava, Z. Tomovski, Appl. Math. Comput. 211, 198 (2009)

    MathSciNet  Google Scholar 

  29. Z. Tomovski, R. Hilfer, H.M. Srivastava, Integr. Transf. Spec. F 21, 797 (2010)

    Article  Google Scholar 

  30. R. Gorenflo, A.A. Kilbas, F. Mainardi, S.V. Rogosin, Mittag-Leffler Functions, Related Topics and Applications (Springer, Berlin, 2014)

  31. A.A. Kilbas, M. Saigo, R.K. Saxena, Integr. Transf. Spec. F 15, 31 (2004)

    Article  Google Scholar 

  32. K.S. Miller, S.G. Samko, Real Anal. Exch. 23, 753 (1997-1998)

    Google Scholar 

  33. D.P. Ahokposi, A. Atangana, D.P. Vermeulen, Eur. Phys. J. Plus 132, 165 (2017)

    Article  Google Scholar 

  34. A. Tateishi, H. Ribeiro, E.K. Lenzi, Front. Phys. 5, 1 (2017)

    Article  Google Scholar 

  35. D. Baleanu, A. Fernandez, Commun. Nonlinear Sci. 59, 444 (2018)

    Article  Google Scholar 

  36. A.J. van der Schaft, Port-Hamiltonian Systems: Network Modeling and Control of Nonlinear Physical Systems, in Advanced Dynamics and Control of Structures and Machines, edited by H. Irschik, K. Schlacher (International Centre for Mechanical Sciences, Springer, Vienna, 2004)

  37. O.P. Agrawal, J. Math. Anal. Appl. 272, 368 (2000)

    Article  ADS  Google Scholar 

  38. C. Li, F. Zeng, Numer. Funct. Anal. Opt. 34, 149 (2013)

    Article  Google Scholar 

  39. T. Abdeljawad, D. Baleanu, J. Nonlinear Sci. Appl. 10, 1098 (2017)

    Article  MathSciNet  Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Arts and Sciences, Cankaya University, 06530, Ankara, Turkey

    Dumitru Baleanu

  2. Institute of Space Sciences, P.O. Box, MG-23, R 76900, Magurele, Bucharest, Romania

    Dumitru Baleanu

  3. Department of Electrical and Computer Engineering, Hakim Sabzevari University, Sabzevar, Iran

    Samaneh Sadat Sajjadi

  4. Department of Electrical Engineering, University of Bojnord, P.O. Box, 94531-1339, Bojnord, Iran

    Amin Jajarmi

  5. Palestine Technical University, College of Arts and Sciences, Department of Physics, P.O. Box 7, Tulkarm, Palestine

    Jihad H. Asad

Authors
  1. Dumitru Baleanu
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  2. Samaneh Sadat Sajjadi
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  3. Amin Jajarmi
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  4. Jihad H. Asad
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Correspondence to Amin Jajarmi.

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Baleanu, D., Sadat Sajjadi, S., Jajarmi, A. et al. New features of the fractional Euler-Lagrange equations for a physical system within non-singular derivative operator. Eur. Phys. J. Plus 134, 181 (2019). https://doi.org/10.1140/epjp/i2019-12561-x

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  • DOI: https://doi.org/10.1140/epjp/i2019-12561-x

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