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

• Authors: Jamshad Ahmad , Syed Tauseef Mohyud-Din , H. M. Srivastava , Xiao-Jun Yang
• Languages of publication: EN

Abstracts

EN

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.

Keywords

EN

Partial differential equations; Local fractionalderivative operators; Mittag-Leffler function; Local fractionaldecomposition method (LFDM)

• Publisher: De Gruyter Open
• Journal: Waves, Wavelets and Fractals
• Year: 2015
• Volume: 1
• Issue: 1

Dates

online

11 - 11 - 2015

accepted

29 - 9 - 2015

received

8 - 8 - 2015

Contributors

author

Jamshad Ahmad

• Department of Mathematics, Faculty of Sciences,
  HITEC University, Taxila, Pakistan

author

Syed Tauseef Mohyud-Din

• Department of Mathematics, Faculty of Sciences,
  HITEC University, Taxila, Pakistan

author

H. M. Srivastava

• Department of Mathematics and Statistics, University
  of Victoria, Victoria, British Columbia V8W 3R4, Canada and
  China Medical University, Taichung 40402, Taiwan, Republic of
  China

author

Xiao-Jun Yang

• China University of
  Mining and Technology, Department of Mathematics and Mechanics,
  Xuzhou, Jiangsu 221008, People’s Republic of China

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Identifiers

DOI

10.1515/wwfaa-2015-0003