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Khan, H., Shah, R., Kumam, P. and Arif, M. (2019) Analytical Solutions of Fractional-Order Heat and Wave Equations by the Natural Transform Decomposition Method. Entropy, 21, Article No. 597.
https://doi.org/10.3390/e21060597

has been cited by the following article:

• TITLE: The Natural Transform Decomposition Method for Solving Fractional Klein-Gordon Equation

  AUTHORS: Mohamed Elbadri

  KEYWORDS: Natural Transform, Adomian Decomposition Method, Fractional Klein-Gordon Equation

  JOURNAL NAME: Applied Mathematics, Vol.14 No.3, March 31, 2023

  ABSTRACT: In this paper, a coupling of the natural transform method and the Admoian decomposition method called the natural transform decomposition method (NTDM), is utilized to solve the linear and nonlinear time-fractional Klein-Gordan equation. The (NTDM), is introduced to derive the approximate solutions in series form for this equation. Solutions have been drawn for several values of the time power. To identify the strength of the method, three examples are presented.