10.57647/

Airy equation with memory involvement via Liouville differential operator

PDF
  • Mehdi Nategh1,
  • Bahram Agheli2,
  • Dumitru Baleanu3,
  • Abdolali Neamaty4,
  1. Department of Mathematics, University of Mazandaran, Babolsar, Iran
  2. Department of Mathematics, Qaemshahr Branch, Islamic Azad University, Qaemshahr, Iran.
  3. Department of Mathematics, C¸ankaya University, Ankara, Turkey.
  4. Department of Mathematics, Qaemshahr Branch, Islamic Azad University, Qaemshahr, Iran

Received: 10-03-2017

Revised: 01-04-2014

Accepted: 04-11-2017

Published in Issue 27-07-2025

Copyright (c) 2025 Mehdi Nategh, Bahram Agheli, Dumitru Baleanu, Abdolali Neamaty (Author)

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Nategh, M., Agheli, B., Baleanu, D., & Neamaty, A. (2025). Airy equation with memory involvement via Liouville differential operator. International Journal of Mathematical Modelling & Computations, 7(2). https://doi.org/10.57647/
Crossref
Scopus
Google Scholar
Europe PMC

Abstract

In this work, a non-integer order Airy equation involving Liouville differential operator is considered. Proposing an undetermined integral solution to the left fractional Airy differential equation, we utilize some basic fractional calculus tools to clarify the closed form. A similar suggestion to the right FADE, converts it into an equation in the Laplace domain. An illustration to the approximation and asymptotic behavior of the integral solution to the left FADE with respect to the existing parameters is presented.

Keywords

  • Fractional Calculus,
  • Liuville differential operator,
  • Airy function,
  • Fractional Airy equation
PDF

References

  1. [1] Aghili. A and Zeinali. H, Solution to fractional schrdinger and Airy differential equations via integral
  2. transforms. British Journal of Mathematics & Computer Science, 4 (18) (2014) 2630-2664.
  3. [2] Assanto. G, Minzoni. A and A & Smyth. N. F, On optical Airy beams in integrable and nonintegrable, Wave Motion, 52 (2015) 183-193.
  4. [3] Besieris. I. M, Shaarawi. A and M & Zamboni-Rached. M, Accelerating Airy beams in the presence
  5. of inhomogeneities, Optics Communications, 369 (2016) 56-64.
  6. [4] Murray. J. D, Asymptotic Analysis. Springer-Verlag,(1974) .
  7. [5] Neamaty. A, Agheli. B and Darzi. R, On the determination of the eigenvalues for Airy fractional
  8. differential equation with turning point, TJMM, 7 (2) (2015) 149-153.
  9. [6] Saka, B. A quatric e-spline collocation method for solving the nonliner SchA¨odinger equation, Appl.
  10. Comput. Math, 14 (1) (2015) 75-86.
  11. [7] S. G. Samko, A. A. Kilbas and O. L. Marichev. Fractional Intergrals and Derivativss, Theory and
  12. Applications. Gordon and Breach Science Publishers, (1993).
  13. [8] Suarez. R. A. B, Vieira. T. A, Yepes. S. V, Gesualdi and M. R. R, Photorefractive and computational
  14. holography in the experimental generation of Airy beams. Optics Communications, 366 (2016) 291-
  15. 300.
  16. [9] Tarasov. Vasily. E, Revieq of some promising fractional physocal models, Int. J. Mod. Phys. B, (27)
  17. (2013) 9-32.
  18. [10] Turkyilmazoglu. M, The Airy equation and its alternative analytic solution. Physica Scripta, 86
  19. (2012).
  20. [11] Uchaikin. V. V, Fractional Derivatives for Physicists and Engineers Volume I Background and
  21. Theory, Springer, (2013).
  22. [12] Vall´ ee. O and Soares. M, Airy Functions And Applications To Physics, Imperial College Press,
  23. (2004)