Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
Browse
8 results
Search Results
Article Citation - WoS: 26Citation - Scopus: 26The Geophysical Kdv Equation: Its Solitons, Complexiton, and Conservation Laws(Springer Heidelberg, 2022) Hosseini, K.; Akbulut, A.; Baleanu, D.; Salahshour, S.; Mirzazadeh, M.; Akinyemi, L.The main goal of the current paper is to analyze the impact of the Coriolis parameter on nonlinear waves by studying the geophysical KdV equation. More precisely, specific transformations are first adopted to derive one-dimensional and operator forms of the governing model. Solitons and complexiton of the geophysical KdV equation are then retrieved with the help of several well-established approaches such as the Kudryashov and Hirota methods. In the end, the new conservation theorem given by Ibragimov is formally employed to extract conservation laws of the governing model. It is shown that by increasing the Coriolis parameter, based on the selected parameter regimes, less time is needed for tending the free surface elevation to zero.Article Citation - WoS: 29Citation - Scopus: 30Monic Chebyshev Pseudospectral Differentiation Matrices for Higher-Order Ivps and Bvps: Applications To Certain Types of Real-Life Problems(Springer Heidelberg, 2022) Abdelhakem, M.; Ahmed, A.; Baleanu, D.; El-kady, M.We introduce new differentiation matrices based on the pseudospectral collocation method. Monic Chebyshev polynomials (MCPs) were used as trial functions in differentiation matrices (D-matrices). Those matrices have been used to approximate the solutions of higher-order ordinary differential equations (H-ODEs). Two techniques will be used in this work. The first technique is a direct approximation of the H-ODE. While the second technique depends on transforming the H-ODE into a system of lower order ODEs. We discuss the error analysis of these D-matrices in-depth. Also, the approximation and truncation error convergence have been presented to improve the error analysis. Some numerical test functions and examples are illustrated to show the constructed D-matrices' efficiency and accuracy.Article Citation - WoS: 4Citation - Scopus: 6Small Amplitude Ion-Acoustic Solitary Waves in a Magnetized Ion-Beam Plasma Under the Effect of Ion and Beam Temperatures(Springer Heidelberg, 2023) Madhukalya, B.; Das, R.; Hosseini, K.; Baleanu, D.; Salahshour, S.In the present research of magnetized plasmas, both rarefactive and compressive solitons are found to exist, based on the values of certain parameters. It has been shown in the present investigation that inclusion of beam temperature into the plasma is in search of the existence of both slow and fast modes for both the cases Q' < 1 and Q' > 1. Furthermore, it is noteworthy to point out that the ion-acoustic soliton is found to exist for ? = U-d sin?/M = beam velocity/phase velocity = 1 as well.Article Citation - WoS: 32Citation - Scopus: 42The 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.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.Article Citation - WoS: 11Citation - Scopus: 21Normalized Lucas Wavelets: an Application To Lane-Emden and Pantograph Differential Equations(Springer Heidelberg, 2020) Koundal, Reena; Srivastava, K.; Baleanu, D.; Kumar, RakeshIn this paper, a novel normalized Lucas wavelet scheme based on tau approach is proposed for the two classes of second-order differential equations, namely Lane-Emden and pantograph equations. The introduced scheme depends on shifted Lucas polynomials (SLPs) and their operational matrix of derivative (which are developed here). The weight function for the orthogonality of Lucas polynomials, and Rodrigues formula are proposed for the first time, which form the basis for the construction of SLPs. Normalized Lucas wavelets are constructed by utilizing SLPs and their novel properties. Literally, the present scheme transforms the given method to a set of nonlinear algebraic equations with undetermined coefficients which are here tackled by tau method. Meanwhile, new treatment of convergence and error analysis is provided for the established approach. Finally, the accuracy and applicability of present scheme is ensured by considering several examples.Article Citation - WoS: 193Citation - Scopus: 220Fractional Calculus: a Survey of Useful Formulas(Springer Heidelberg, 2013) Trujillo, J. J.; Rivero, M.; Machado, J. A. T.; Baleanu, D.; Valerio, D.This paper presents a survey of useful, established formulas in Fractional Calculus, systematically collected for reference purposes.Article Citation - WoS: 36Citation - Scopus: 41Derivation of a Fractional Boussinesq Equation for Modelling Unconfined Groundwater(Springer Heidelberg, 2013) Jafari, H.; Baleanu, D.; Mehdinejadiani, B.In this manuscript, a fractional Boussinesq equation is obtained by assuming power-law changes of flux in a control volume and using a fractional Taylor series. Furthermore, it was assumed that the average thickness of the watery layer of an aquifer is constant, and the linear fractional Boussinesq equation was derived. Unlike classical Boussinesq equation, due to the non-locality property of fractional derivatives, the parameters of the fractional Boussinesq equation are constant and scale-invariant. In addition, the fractional Boussinesq equation has two various fractional orders of differentiation with respect to x and y that indicate the degree of heterogeneity in the x and y directions, respectively.Article Citation - WoS: 8Citation - Scopus: 10Variation of Constant Formula for the Solution of Interval Differential Equations of Non-Integer Order(Springer Heidelberg, 2017) Ahmadian, A.; Baleanu, D.; Salahshour, S.In the recent years some efforts were made to propose simple and well-behaved fractional derivatives that inherits the classical properties from the first order derivative. Therefore, we propose in this research a new strategy to acquire interval solution of fractional interval differential equations (FIDEs) under interval fractional conformable derivative. This scheme is developed based on a variation of the constant formula to achieve the solution explicitly. The important characteristic of this technique is that it helps us to find a solution with decreasing length of its support which is critical for the solutions based on the interval or fuzzy notions. Two examples are experienced to illustrate our approach and validate it.