Geodesic
A new analytical approximate solution of fractional coupled Korteweg-de Vries system
Yugoslav journal of operations research, Tome 33 (2023) no. 4, p. 667 .

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The main objective of this work is to present a modification of the Mittag-Leffler function to deduce a relatively new analytical approximate method (for short MMLFM) able to solve time-fractional nonlinear partial differential equations (PDEs). Moreover, we employ the MMLFM to solve the time-fractional coupled Korteweg–de Vries (KdV) model described by two nonlinear fractional partial differential equations (FPDEs) based upon Caputo fractional derivative (CFD). The simulation of projected results is presented in some figures and tables. Furthermore, we compare our solutions when α = 1 with known exact solutions which indicate a good agreement, in addition, we compare our outcomes with the results obtained by other methods in the literature such as the Natural decomposing method (NDM) and homotopy decomposition method (HDM) in order to prove the reliability and efficiency of our used method. Also, we display solutions with different values of α to present the effect of the fractional order on the proposed problem. The results of this article reveal the advantages of the MMLFM, which is simple, reliable, accurate, needs simple mathematical computations, is rapidly convergent to the exact solution, have a straightforward and easy algorithm compared 668 H.M. Ali et al. / A New Analytical Approximate Solution to other analytical methods to study linear and nonlinear FPDEs, which makes this technique suited for real industrial or medical applications.
Classification : 35R11, 33E12, 35Q92, 35C10
Keywords: Fractional coupled Korteweg-de Vries equation, fractional partial differential, equations, Mittag-Leffler function, nonlinear problems, approximate solutions 
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     author = {Hegagi Mohamed Ali and Alaa Hassan Noreldeen and Ali Shahat Ali},
     title = {A new analytical approximate solution of fractional coupled {Korteweg-de} {Vries} system},
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     year = {2023},
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     url = {http://geodesic.mathdoc.fr/item/YJOR_2023_33_4_a7/}
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Hegagi Mohamed Ali; Alaa Hassan Noreldeen; Ali Shahat Ali. A new analytical approximate solution of fractional coupled Korteweg-de Vries system. Yugoslav journal of operations research, Tome 33 (2023) no. 4, p. 667 . http://geodesic.mathdoc.fr/item/YJOR_2023_33_4_a7/