Browsing by Author "Park, Choonkil"

Now showing 1 - 4 of 4

Citation Count: Sadri, Khadijeh;...et.al. (2022). "Designing a matrix collocation method for fractional delay integro-differential equations with weakly singular kernels based on vieta–fibonacci polynomials", Fractal and Fractional, Vol.6, No.1.
Designing a matrix collocation method for fractional delay integro-differential equations with weakly singular kernels based on vieta–fibonacci polynomials
(2022) Sadri, Khadijeh; Hosseini, Kamyar; Baleanu, Dumitru; Salahshour, Soheil; Park, Choonkil; 56389
In 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.
Citation Count: Park, Choonkil...et al. (2020). "Novel hyperbolic and exponential ansatz methods to the fractional fifth-order Korteweg-de Vries equations". ADVANCES IN DIFFERENCE EQUATIONS. Vol: 2020, No: 1.
Novel hyperbolic and exponential ansatz methods to the fractional fifth-order Korteweg-de Vries equations
(2020) Park, Choonkil; Nuruddeen, R., I; Ali, Khalid K.; Muhammad, Lawal; Osman, M. S.; Baleanu, Dumitru; 56389
This paper aims to investigate the class of fifth-order Korteweg-de Vries equations by devising suitable novel hyperbolic and exponential ansatze. The class under consideration is endowed with a time-fractional order derivative defined in the conformable fractional derivative sense. We realize various solitons and solutions of these equations. The fractional behavior of the solutions is studied comprehensively by using 2D and 3D graphs. The results demonstrate that the methods mentioned here are more effective in solving problems in mathematical physics and other branches of science.
Citation Count: Baleanu, Dumitru...et al. (2021). "The (2+1)-dimensional hyperbolic nonlinear Schrodinger equation and its optical solitons", AIMS Mathematics, Vol. 6, No. 9, pp. 9568-9581.
The (2+1)-dimensional hyperbolic nonlinear Schrodinger equation and its optical solitons
(2021) Baleanu, Dumitru; Hosseini, Kamyar; Salahshour, Soheil; Sadri, Khadijeh; Mirzazadeh, Mohammad; Park, Choonkil; Ahmadian, Ali; 56389
A 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.
Citation Count: Hosseini, Kamyar...et.al. (2022). "The Caputo-Fabrizio time-fractional Sharma-Tasso-Olver-Burgers equation and its valid approximations", Communications in Theoretical Physics, Vol.74, No.7.
The Caputo-Fabrizio time-fractional Sharma-Tasso-Olver-Burgers equation and its valid approximations
(2022) Hosseini, Kamyar; Ilie, Mousa; Mirzazadeh, Mohammad; Baleanu, Dumitru; Park, Choonkil; Salahshour, Soheil; 56389
Studying the dynamics of solitons in nonlinear time-fractional partial differential equations has received substantial attention, in the last decades. The main aim of the current investigation is to consider the time-fractional Sharma-Tasso-Olver-Burgers (STOB) equation in the Caputo-Fabrizio (CF) context and obtain its valid approximations through adopting a mixed approach composed of the homotopy analysis method (HAM) and the Laplace transform. The existence and uniqueness of the solution of the time-fractional STOB equation in the CF context are investigated by demonstrating the Lipschitz condition for φx,t;u as the kernel and giving some theorems. To illustrate the CF operator effect on the dynamics of the obtained solitons, several two- and three-dimensional plots are formally considered. It is shown that the mixed approach is capable of producing valid approximations to the time-fractional STOB equation in the CF context.