WoS İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653
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Article Citation - WoS: 15Citation - Scopus: 14Designing a Matrix Collocation Method for Fractional Delay Integro-Differential Equations With Weakly Singular Kernels Based on Vieta-Fibonacci Polynomials(Mdpi, 2022) Hosseini, Kamyar; Baleanu, Dumitru; Salahshour, Soheil; Park, Choonkil; Sadri, KhadijehIn the present work, the numerical solution of fractional delay integro-differential equations (FDIDEs) with weakly singular kernels is addressed by designing a Vieta-Fibonacci collocation method. These equations play immense roles in scientific fields, such as astrophysics, economy, control, biology, and electro-dynamics. The emerged fractional derivative is in the Caputo sense. By resultant operational matrices related to the Vieta-Fibonacci polynomials (VFPs) for the first time accompanied by the collocation method, the problem taken into consideration is converted into a system of algebraic equations, the solving of which leads to an approximate solution to the main problem. The existence and uniqueness of the solution of this category of fractional delay singular integro-differential equations (FDSIDEs) are investigated and proved using Krasnoselskii's fixed-point theorem. A new formula for extracting the VFPs and their derivatives is given, and the orthogonality of the derivatives of VFPs is easily proved via it. An error bound of the residual function is estimated in a Vieta-Fibonacci-weighted Sobolev space, which shows that by properly choosing the number of terms of the series solution, the approximation error tends to zero. Ultimately, the designed algorithm is examined on four FDIDEs, whose results display the simple implementation and accuracy of the proposed scheme, compared to ones obtained from previous methods. Furthermore, the orthogonality of the VFPs leads to having sparse operational matrices, which makes the execution of the presented method easy.Article Citation - WoS: 20Citation - Scopus: 24The (2+1)-Dimensional Hyperbolic Nonlinear Schrodinger Equation and Its Optical Solitons(Amer inst Mathematical Sciences-aims, 2021) Hosseini, Kamyar; Salahshour, Soheil; Sadri, Khadijeh; Mirzazadeh, Mohammad; Park, Choonkil; Ahmadian, Ali; Baleanu, Umitru; Baleanu, DumitruA comprehensive study on the (2+1)-dimensional hyperbolic nonlinear Schrodinger (2D-HNLS) equation describing the propagation of electromagnetic fields in self-focusing and normally dispersive planar wave guides in optics is conducted in the current paper. To this end, after reducing the 2D-HNLS equation to a one-dimensional nonlinear ordinary differential (1D-NLOD) equation in the real regime using a traveling wave transformation, its optical solitons are formally obtained through a group of well-established methods such as the exponential and Kudryashov methods. Some graphical representations regarding optical solitons that are categorized as bright and dark solitons are considered to clarify the dynamics of the obtained solutions. It is noted that some of optical solitons retrieved in the current study are new and have been not retrieved previously.Article Citation - WoS: 28Citation - Scopus: 29Solitons and Jacobi Elliptic Function Solutions To the Complex Ginzburg-Landau Equation(Frontiers Media Sa, 2020) Hosseini, Kamyar; Mirzazadeh, Mohammad; Osman, M. S.; Al Qurashi, Maysaa; Baleanu, DumitruThe complex Ginzburg-Landau (CGL) equation which describes the soliton propagation in the presence of the detuning factor is firstly considered; then its solitons as well as Jacobi elliptic function solutions are obtained systematically using a modified Jacobi elliptic expansion method. In special cases, several dark and bright soliton solutions to the CGL equation are retrieved when the modulus of ellipticity approaches unity. The results presented in the current work can help to complete previous studies on the complex Ginzburg-Landau equation.Article Citation - WoS: 13Citation - Scopus: 15N-Wave and Other Solutions To the B-Type Kadomtsev-Petviashvili Equation(Vinca inst Nuclear Sci, 2019) Hosseini, Kamyar; Samavat, Majid; Mirzazadeh, Mohammad; Eslami, Mostafa; Moradi, Mojtaba; Baleanu, Dumitru; Inc, MustafaThe present article studies a B-type Kadomtsev-Petviashvili equation with certain applications in the fluids. Stating with the Hirota's bilinear form and adopting reliable methodologies, a group of exact solutions such as the N-wave and other solutions to the B-type Kadomtsev-Petviashvili equation is formally derived. Some figures in two and three dimensions are given to illustrate the characteristics of the obtained solutions. The results of the current work actually help to complete the previous studies about the B-type Kadomtsev-Petviashvili equation.Article Citation - WoS: 11Citation - Scopus: 17Bivariate Chebyshev Polynomials of the Fifth Kind for Variable-Order Time-Fractional Partial Integro-Differential Equations With Weakly Singular Kernel(Springer, 2021) Hosseini, Kamyar; Baleanu, Dumitru; Ahmadian, Ali; Salahshour, Soheil; Sadri, KhadijehThe shifted Chebyshev polynomials of the fifth kind (SCPFK) and the collocation method are employed to achieve approximate solutions of a category of the functional equations, namely variable-order time-fractional weakly singular partial integro-differential equations (VTFWSPIDEs). A pseudo-operational matrix (POM) approach is developed for the numerical solution of the problem under study. The suggested method changes solving the VTFWSPIDE into the solution of a system of linear algebraic equations. Error bounds of the approximate solutions are obtained, and the application of the proposed scheme is examined on five problems. The results confirm the applicability and high accuracy of the method for the numerical solution of fractional singular partial integro-differential equations.