Analytic solutions of the Helmholtz and Laplace equations by using local fractional derivative operators

Jamshad Ahmad; Syed Tauseef Mohyud-Din; H. M. Srivastava; Xiao-Jun Yang

Waves, Wavelets and Fractals (2015)

  • Volume: 1, Issue: 1
  • ISSN: 2449-5557

Abstract

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In this paper we develop analytical solutions for the Helmholtz and Laplace equations involving local fractional derivative operators. We implement the local fractional decomposition method (LFDM) for finding the exact solutions. The iteration procedure is based upon the local fractional derivative sense. The numerical results, whichwe present in this paper, show that the methodology used provides an efficient and simple tool for solving fractal phenomena arising in mathematical physics and engineering. Several illustrative examples are also provided.

How to cite

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Jamshad Ahmad, et al. "Analytic solutions of the Helmholtz and Laplace equations by using local fractional derivative operators." Waves, Wavelets and Fractals 1.1 (2015): null. <http://eudml.org/doc/276455>.

@article{JamshadAhmad2015,
abstract = {In this paper we develop analytical solutions for the Helmholtz and Laplace equations involving local fractional derivative operators. We implement the local fractional decomposition method (LFDM) for finding the exact solutions. The iteration procedure is based upon the local fractional derivative sense. The numerical results, whichwe present in this paper, show that the methodology used provides an efficient and simple tool for solving fractal phenomena arising in mathematical physics and engineering. Several illustrative examples are also provided.},
author = {Jamshad Ahmad, Syed Tauseef Mohyud-Din, H. M. Srivastava, Xiao-Jun Yang},
journal = {Waves, Wavelets and Fractals},
keywords = {Partial differential equations; Local fractional derivative operators; Mittag-Leffler function; Local fractional decomposition method (LFDM)},
language = {eng},
number = {1},
pages = {null},
title = {Analytic solutions of the Helmholtz and Laplace equations by using local fractional derivative operators},
url = {http://eudml.org/doc/276455},
volume = {1},
year = {2015},
}

TY - JOUR
AU - Jamshad Ahmad
AU - Syed Tauseef Mohyud-Din
AU - H. M. Srivastava
AU - Xiao-Jun Yang
TI - Analytic solutions of the Helmholtz and Laplace equations by using local fractional derivative operators
JO - Waves, Wavelets and Fractals
PY - 2015
VL - 1
IS - 1
SP - null
AB - In this paper we develop analytical solutions for the Helmholtz and Laplace equations involving local fractional derivative operators. We implement the local fractional decomposition method (LFDM) for finding the exact solutions. The iteration procedure is based upon the local fractional derivative sense. The numerical results, whichwe present in this paper, show that the methodology used provides an efficient and simple tool for solving fractal phenomena arising in mathematical physics and engineering. Several illustrative examples are also provided.
LA - eng
KW - Partial differential equations; Local fractional derivative operators; Mittag-Leffler function; Local fractional decomposition method (LFDM)
UR - http://eudml.org/doc/276455
ER -

References

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