Matematik Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413
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Article Citation - WoS: 7Citation - Scopus: 6New Solutions of Nonlinear Dispersive Equation in Higher-Dimensional Space With Three Types of Local Derivatives(Mdpi, 2022) Hashemi, Mir Sajjad; Jarad, Fahd; Akgul, AliThe aim of this paper is to use the Nucci's reduction method to obtain some novel exact solutions to the s-dimensional generalized nonlinear dispersive mK(m,n) equation. To the best of the authors' knowledge, this paper is the first work on the study of differential equations with local derivatives using the reduction technique. This higher-dimensional equation is considered with three types of local derivatives in the temporal sense. Different types of exact solutions in five cases are reported. Furthermore, with the help of the Maple package, the solutions found in this study are verified. Finally, several interesting 3D, 2D and density plots are demonstrated to visualize the nonlinear wave structures more efficiently.Article Citation - WoS: 9Citation - Scopus: 9Fractional Propagation of Short Light Pulses in Monomode Optical Fibers: Comparison of Beta Derivative and Truncated M-Fractional Derivative(Asme, 2022) Jhangeer, Adil; Awrejcewicz, Jan; Baleanu, Dumitru; Tahir, Sana; Riaz, Muhammad BilalThis study is dedicated to the computation and analysis of solitonic structures of a nonlinear Sasa-Satsuma equation that comes in handy to understand the propagation of short light pulses in the monomode fiber optics with the aid of beta derivative and truncated M-fractional derivative. We employ a new direct algebraic technique for the nonlinear Sasa-Satsuma equation to derive novel soliton solutions. A variety of soliton solutions are retrieved in trigonometric, hyperbolic, exponential, rational forms. The vast majority of obtained solutions represent the lead of this method on other techniques. The prime advantage of the considered technique over the other techniques is that it provides more diverse solutions with some free parameters. Moreover, the fractional behavior of the obtained solutions is analyzed thoroughly by using two and three-dimensional graphs. This shows that for lower fractional orders, i.e., beta = 0.1, the magnitude of truncated Mfractional derivative is greater whereas for increasing fractional orders, i.e., beta = 0.7 and beta = 0.99, the magnitude remains the same for both definitions except for a phase shift in some spatial domain that eventually vanishes and two curves coincide.Article Citation - WoS: 88Citation - Scopus: 94Optical Solitons Possessing Beta Derivative of the Chen-Lee Equation in Optical Fibers(Frontiers Media Sa, 2019) Inc, Mustafa; Aliyu, Aliyu Isa; Baleanu, Dumitru; Yusuf, AbdullahiThis research obtains some new optical soliton solutions with beta derivative for Chen-Lee-Liu equation (CLL) in optical fibers. Three integration schemes which are Ricatti-Bernoulli (RB) sub-ODE, generalized Bernoulli (GB) sub-ODE and generalized tanh (GT) methods are applied to reach such solutions. The constraints conditions for the existence of soliton solutions are reported. The solutions are obtained using newly introduced fractional derivative called beta derivative. Numerical simulations of some of the obtained solutions are illustrated.Article Citation - WoS: 52Citation - Scopus: 61Optical Solitons With M-Truncated and Beta Derivatives in Nonlinear Optics(Frontiers Media Sa, 2019) Inc, Mustafa; Baleanu, Dumitru; Yusuf, AbdullahiThis paper studies optical solitons with M-truncated and beta derivatives (BD) for the Complex Ginzburg-Landau equation (CGLE) with Kerr Law nonlinearity. Two well-known integration schemes which are generalized tanh method (GTM) and generalized Bernoulli sub-ODE method (GBM) are utilized to extract such optical soliton solutions. For the successful existence of the solutions, the constraints conditions have been presented. The discussion for the physical features of the obtained solutions is reported.