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Browsing by Author "Park, C."

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    Citation - WoS: 3
    Citation - Scopus: 4
    Further Studies on Ordinary Differential Equations Involving the M-Fractional Derivative
    (Amer inst Mathematical Sciences-aims, 2022) Khoshkenar, A.; Ilie, M.; Hosseini, K.; Baleanu, D.; Salahshour, S.; Park, C.; Lee, J. R.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
    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.
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    Citation - WoS: 31
    Citation - Scopus: 40
    The Generalized Complex Ginzburg-Landau Model and Its Dark and Bright Soliton Solutions
    (Springer Heidelberg, 2021) Hosseini, K.; Mirzazadeh, M.; Baleanu, D.; Raza, N.; Park, C.; Ahmadian, A.; Salahshour, S.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
    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.