2015 **Abstract:** Abstract:The purpose of this short paper is to show the invalidity of a Fourier series expansion of fractional order as derived by G. Jumarie in a series of papers. In his work the exponential functions e inωx are replaced by the Mittag-Leffler functions

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“…Existence of the exact solution of the nonlinear Sawada-Kotera equation modeled with Caputo time fractional derivative is proven in this section. Recall that similar analysis was performed in other works [22,23]. We focus our attention on the following Sawada-Kotera model expressed as…”

confidence: 94%

“…Existence of the exact solution of the nonlinear Sawada-Kotera equation modeled with Caputo time fractional derivative is proven in this section. Recall that similar analysis was performed in other works [22,23]. We focus our attention on the following Sawada-Kotera model expressed as…”

confidence: 94%

“…The ideal solution of the Equation ( 15) is 𝑈 (𝑥, 𝑡) = 𝐸 , (𝑥 − 𝑡 /2). The function 𝐸 , (𝑧) , is called the Mittag-Leffler function [39] and is described as 𝐸 , (𝑧) = Figure 2. A 1D plot of the absolute error between approximate (fx) and exact (sol) solutions is depicted on the left-hand for t = x changed in the solution, Equation ( 14).…”

confidence: 99%

“…However, in Ref. [39] the authors state that, in fractional calculus, this kind of trigonometry identity does not hold. In this example, we have computationally proven that the above identity is no longer valid in fractional calculus, i.e.,…”

confidence: 99%