DOI: https://doi.org/10.14710/jfma.v3i1.7411

FUNGSI WRIGHT SEBAGAI SOLUSI ANALITIK PERSAMAAN DIFUSI-GELOMBANG FRAKSIONAL PADA MEDIA VISKOELASTIS

*Ray Novita Yasa  -  Sekolah Tinggi Sandi Negara, Indonesia
Agus Yodi Gunawan  -  Institut Teknologi Bandung, Indonesia

Citation Format:
Abstract

A fractional diffusion-wave equations in a fractional viscoelastic media can be constructed by using equations of motion and kinematic equations of viscoelastic
material in fractional order. This article concerns the fractional diffusion-wave equations in the fractional viscoelastic media for semi-infinite regions that satisfies signalling boundary value problems. Fractional derivative was used in Caputo sense. The analytical solution of the fractional diffusion-wave equation in the fractional viscoelastic media was solved by means of Laplace transform techniques in the term of Wright function for simple form solution. For general parameters, Numerical Inverse Laplace Transforms (NILT) was used to determine the solution.

Fulltext View|Download

Article Metrics:

Article Info
Section: FUNDAMENTAL MATHEMATICS AND APPLICATIONS
Language : ID
Recent articles
EASY ENSEMMBLE WITH RANDOM FOREST TO HANDLE IMBALANCED DATA IN CLASSIFICATION ANALISIS TARIF PREMI DAN ASUMSI LOADING PADA PRODUK ASURANSI DWIGUNA BEASISWA KARAKTERISASI MODUL CYCLICALLY PURE (CP)-INJEKTIF More recent articles
  1. Nutting, P.G. 1921: A new general law of deformation, Journal of The Franklin Institute, Vol. 191, Edisi 5, 679-685
  2. Blair, G. dan Reiner, M.. (1951). The rheological law underlying the Nutting equation. Flow Turbulence and Combustion - Flow Turbul Combust. 2. 225-234. 10.1007/BF00411984
  3. Rogosin, S. dan Mainardi, F. 2014: George William Scott Blair the pioneer of fractional calculus in rheology. Communications in Applied and Industrial Mathematics, Vol. 6, No. 1.-481; ISSN 2038-0909; DOI: 10.1685/journal.caim.481
  4. Nigmatullin, R. R. 1986: The realization of the generalized transfer equation in a medium with fractal geometry, Physica Status Solidi B, 133, 425430; DOI: 10.1002/pssb.2221330150
  5. Mainardi, F., Luchko, Y., dan Pagnini, G. 2001: The fundamental solution of the spacetime fractional diffusion equation, An International Journal for Theory and Applications, Vol. 4, No. 2, 153-192; ISSN 1311-0454
  6. Mainardi, F., dan Pagnini, G. 2003: The wright function as solutionsof the time-fractional diffusion equation, Applied Mathematics and Computation, Vol. 141, Edisi 1, 51-62; dx.doi.org/10.1016/S0096-3003(02)00320-X
  7. Povstenko, Y. 2011: Non-axisymmetric solutions to time-fractional diffusion-wave equation in an infinite cylinder, Fractional Calculus and Applied Analysis, Vol. 14, No. 3, 418-435; DOI: 10.2478/s13540-011-0026-4
  8. A. Bradji, A new analysis for the convergence of the gradient discretization method for multidimensional time fractional diffusion and diffusion-wave equations, Computers and Mathematics with Applications (2019), https://doi.org/10.1016/j.camwa.2019.11.001
  9. Y.Zheng, Z. Zhao, The time discontinuous space-time finite element methode for fractional diffusion-wave equation, Appl. Numer. Math. (2019), https://doi.org/10.1016/j.apnum.2019.09.007
  10. Tramontana V, et al. An application of Wright functions to the photon propagation. J Quant Spectrosc Radiat Transfer (2013), http://dx.doi.org/10.1016/j.jqsrt.2013.03.008
  11. Elsaid, A., Latief, M.S.A, Maneea, M. 2016: Similarrity Solutions for Multiterm Time- Fractional Diffusion Equation, Advances in Mathematical Physics, Hindawi Publishing Corporation, http://dx.doi.org/10.1155/2016/7304659
  12. Mainardi, F. 2010: Fractional calculus and wave in liear viscoelasticity, An introduction to mathematical models, ISBN-101-84816-329-0, London, Imperial College Press
  13. Podlubny, I. 1999: Fractional differential equation, Mathematics in Science and Engineering, Vol. 198, ISBN 0-12-558840-2, San Diego, California, Academic Press
  14. Wong, R. dan Zhao, Y.-Q. 1999: Smoothing of Stokes’ discontinuity for the generalized Bessel function, Proceedings of the Royal Society of London A: Mathematical, Physical
  15. and Engineering Sciences 455, 1381-1400; DOI: 10.1098/rspa.1999.0365
  16. Choksi, H., dan Timol, M.G., 2014: Similarity solution for partial differential equation of fractional order, International Journal of Engineering and Innovative Technology (IJEIT), Vol. 4, Edisi 2, ISSN 2277-3754
  17. Sheng, H., Li, Y., dan Chen, Y.-Q. 2010: Application of numerical inverse Laplace transform algorithms in fractional calculus, Journal of The Franklin Institute, 348, 315-330;
  18. DOI: 10.1016/j.jfranklin.2010.11.009
  19. Rani, D., Mishra, V., Numerical Inverse Laplace Transform based on Bernoulli Polynomials Operational Matrix for Solving Nonlinear Differential Equations, Results in Physics
  20. (2019), doi: https://doi.org/10.1016/j.rinp.2019.102836
  21. N.U. Khan, T. Usman and M. Aman, Some properties concerning the analysis of generalized Wright function, Journal of Computational and Applied Mathematics (2020), doi: https://doi.org/10.1016/j.cam.2020.112840
  22. Brancik, L., dan Smith, N. 2015: Two approaches to derive approximate formulae of NILT method with generalization, IEEE, DOI: 10.1109/MIPRO.2015.7160256

Last update:

No citation recorded.

Last update:

No citation recorded.