Have a personal or library account? Click to login
On the Elzaki transform and its applications in fractional free electron laser equation Cover

On the Elzaki transform and its applications in fractional free electron laser equation

Open Access
|Feb 2020

References

  1. [1] G. Dattoli, L. Gianessi, L. Mezi, D. Tocci, R. Colai, FEL time-evolution operator, Nucl. Instr. Methods A, 304 (1991), 541–544.10.1016/0168-9002(91)90926-H
  2. [2] Tarig. M. Elzaki, The New Integral Transform “Elzaki Transform” fundamental properties investigations and applications, GJPAM, 7 (1) (2011), 57–64.
  3. [3] Tarig M. Elzaki, Application of New Transform “Elzaki Transform” to Partial Differential Equations, GJPAM, 7 (1) (2011), 65–70.
  4. [4] M. Eslaminasab, S. Abbasbandy, Study on usage of Elzaki transform for the ordinary differential equations with non-constant coefficients, Int. J. Ind. Math., 7 (3) 2015, Article ID IJIM-00670 (5 pages).
  5. [5] R. Garra, R. Goreno, F. Polito, Z. Tomovski, Hilfer-Prabhakar Derivatives and Some Applications, Appl. Math. Comput., 242 (1) (2014), 576–589.10.1016/j.amc.2014.05.129
  6. [6] R. Gorenflo, F. Mainardi, Fractional calculus: integral and differential equations of fractional order, In A. Carpinteri and F. Mainardi Fractals and Fractional Calculus in Continuum Mechanics, Springer-Verlag, Wien, (1997), 223–276.
  7. [7] R. Hilfer, Fractional calculus and regular variation in thermodynamics, In R. Hilfer, editor, Applications of Fractional Calculus in Physics, 429, Singapore, 2000. World Scientific.10.1142/9789812817747_0009
  8. [8] A. A. Kilbas, M. Saigo, R. K. Saxena, Generalized Mittag-Leffler function and generalized fractional calculus operators, Integral Transform Spec. Funct., 15 (1) (2004), 31–49.10.1080/10652460310001600717
  9. [9] A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and Applications of the Fractional Differential Equations, North-Holland Math. Stud., 204 (2006).
  10. [10] D. Kumar, J. Singh, M. A. Qurashi, D. Baleanu, Analysis of Logistic Equation pertaining to a new fractional derivative with non-singular kernel, Adv. Mech. Eng., 9 (2) (2017), 1–8.10.1177/1687814017690069
  11. [11] D. Kumar, J. Singh, D. Baleanu, A new fractional model for convective straight fins with temperature-dependent thermal conductivity, Thermal Sci., 22 (6B) (2018), 2791–2802.10.2298/TSCI170129096K
  12. [12] I. Podlubny, Fractional Differential Equations, Academic Press, New York, 1999.
  13. [13] Y. Z. Povstenko, Evolution of the initial box-signal for time-fractional diffusion-wave equation in a case of different spatial dimensions, Physica A, 389 (1) (2010), 4696–4707.10.1016/j.physa.2010.06.049
  14. [14] T. R. Prabhakar, A singular integral equation with a generalized Mittag-Leffler function in the kernel, Yokohama Math. J., 19 (1971), 7–15.
  15. [15] S. G. Samko, A. A. Kilbas, O. I. Marichev, Fractional integrals and derivatives, Gordon and Breach Science, Yverdon, 1993.
  16. [16] T. Sandev, R. Metzler, Z. Tomovski, Fractional diffusion equation with a generalized Riemann-Liouville time fractional derivative, J. Phys. A, 44 (25) (2011), 255203.10.1088/1751-8113/44/25/255203
  17. [17] J. Singh, D. Kumar, J. J. Nieto, Analysis of an El Nino Southern Oscillation model with a new fractional derivative, Chaos Solitons Fractals, 99 (2017), 109–115.10.1016/j.chaos.2017.03.058
  18. [18] J. Singh, D. Kumar, D. Baleanu, Analysis of a new fractional model for damped Burger equations, Open Phys., 15 (2017), 35–41.10.1515/phys-2017-0005
  19. [19] H. M. Srivastava, Z. Tomovski, Fractional calculus with an integral operator containing a generalized Mittag-Leffler function in the kernel, Appl. Math.Comput., 211 (1) (2009), 198–210.10.1016/j.amc.2009.01.055
  20. [20] Z. Tomovski, R. Hilfer, H. M. Srivastava,Fractional and operational calculus with generalized fractional derivative operators and Mittag-Leffler type functions, Integral Transform Spec. Funct., 21 (11) (2010), 797–814.10.1080/10652461003675737
  21. [21] Y. Zhou, F. Jiao, Nonlocal Cauchy problem for fractional evolution equations, Nonlinear Anal Real World Appl., 11 (5) (2010), 4465–4475.10.1016/j.nonrwa.2010.05.029
Language: English
Page range: 419 - 429
Submitted on: Jan 9, 2019
|
Published on: Feb 27, 2020
In partnership with: Paradigm Publishing Services
Publication frequency: 2 issues per year

© 2020 Yudhveer Singh, Vinod Gill, Sunil Kundu, Devendra Kumar, published by Sapientia Hungarian University of Transylvania
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.