Browsing by Author "Park, C."

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Further studies on ordinary differential equations involving the M-fractional derivative
(2022) Khoshkenar, A.; Ilie, M.; Hosseini, K.; Baleanu, D.; Salahshour, S.; Park, C.; Lee, J.R.; 56389
In the current paper, the power series based on the M-fractional derivative is formally introduced. More peciesely, the Taylor and Maclaurin expansions are generalized for fractional-order differentiable functions in accordance with the M-fractional derivative. Some new definitions, theorems, and corollaries regarding the power series in the M sense are presented and formally proved. Several ordinary differential equations (ODEs) involving the M-fractional derivative are solved to examine the validity of the results presented in the current study.
The generalized complex Ginzburg–Landau model and its dark and bright soliton solutions
(2021) Baleanu, Dumitru; Mirzazadeh, M.; Baleanu, Dumitru; Raza, N.; Park, C.; Ahmadian, A.; Salahshour, S.; 56389
In the present work, the generalized complex Ginzburg–Landau (GCGL) model is considered and its 1-soliton solutions involving different wave structures are retrieved through a series of newly well-organized methods. More exactly, after considering the GCGL model, its 1-soliton solutions are obtained using the exponential and Kudryashov methods in the presence of perturbation effects. As a case study, the effect of various parameter regimes on the dynamics of the dark and bright soliton solutions is analyzed in three- and two-dimensional postures. The validity of all the exact solutions presented in this study has been examined successfully through the use of the symbolic computation system.