Geodesic
Time fractional Kupershmidt equation: symmetry analysis and explicit series solution with convergence analysis
Communications in Mathematics, Tome 27 (2019) no. 2, pp. 171-185.

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In this work, the fractional Lie symmetry method is applied for symmetry analysis of time fractional Kupershmidt equation. Using the Lie symmetry method, the symmetry generators for time fractional Kupershmidt equation are obtained with Riemann-Liouville fractional derivative. With the help of symmetry generators, the fractional partial differential equation is reduced into the fractional ordinary differential equation using Erdélyi-Kober fractional differential operator. The conservation laws are determined for the time fractional Kupershmidt equation with the help of new conservation theorem and fractional Noether operators. The explicit analytic solutions of fractional Kupershmidt equation are obtained using the power series method. Also, the convergence of the power series solutions is discussed by using the implicit function theorem.
Classification : 26A33, 34A08, 76M60
Keywords: Time fractional Kupershmidt equation; Fractional Lie symmetry method; Riemann-Lioville's fractional derivative; Conservation laws; Power series solution. 
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     author = {Chauhan, Astha and Arora, Rajan},
     title = {Time fractional {Kupershmidt} equation: symmetry analysis and explicit series solution with convergence analysis},
     journal = {Communications in Mathematics},
     pages = {171--185},
     publisher = {mathdoc},
     volume = {27},
     number = {2},
     year = {2019},
     mrnumber = {4058172},
     zbl = {1464.34018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/COMIM_2019__27_2_a6/}
}
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Chauhan, Astha; Arora, Rajan. Time fractional Kupershmidt equation: symmetry analysis and explicit series solution with convergence analysis. Communications in Mathematics, Tome 27 (2019) no. 2, pp. 171-185. http://geodesic.mathdoc.fr/item/COMIM_2019__27_2_a6/