Browsing by Author "Sadri, Khadijeh"

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Citation Count: Sadri, Khadijeh...et.al. (2023). "A pseudo-operational collocation method for variable-order time-space fractional KdV-Burgers-Kuramoto equation", Mathematical Methods In The Applied Sciences, Vol.46, No.8, pp.8759-8778.
A pseudo-operational collocation method for variable-order time-space fractional KdV-Burgers-Kuramoto equation
(2023) Sadri, Khadijeh; Hosseini, Kamyar; Hincal, Evren; Baleanu, Dumitru; Salahshour, Soheil; 56389
The idea of this work is to provide a pseudo-operational collocation scheme to deal with the solution of the variable-order time-space fractional KdV-Burgers-Kuramoto equation (VOSTFKBKE). Such the fractional partial differential equation (FPDE) has three characteristics of dissipation, dispersion, and instability, which make this equation is used to model many phenomena in diverse fields of physics. Numerical solutions are sought in a linear combination of two-dimensional Jacobi polynomials as basis functions. In order to approximate unknown functions in terms of the basis vector, pseudo-operational matrices are constructed to avoid integration. An error bound of the residual function is estimated in a Jacobi-weighted space in the L2$$ {L}<^>2 $$ norms. Numerical results are compared with exact ones and those reported by other researchers to demonstrate the effectiveness of the recommended method.
Citation Count: Sadri, Khadijeh...et.al. (2023). "A robust scheme for Caputo variable-order time-fractional diffusion-type equations", Journal Of Thermal Analysis And Calorimetry, Vol.148, No.12, pp.5747-5764.
A robust scheme for Caputo variable-order time-fractional diffusion-type equations
(2023) Sadri, Khadijeh; Hosseini, Kamyar; Baleanu, Dumitru; Salahshour, Sohei; Hincal, Evren; 56389
The focus of this work is to construct a pseudo-operational Jacobi collocation scheme for numerically solving the Caputo variable-order time-fractional diffusion-type equations with applications in applied sciences. Modeling scientific phenomena in the context of fluid flow problems, curing reactions of thermosetting systems, solid oxide fuel cells, and solvent diffusion into heavy oils led to the appearance of these equations. For this reason, the numerical solution of these equations has attracted a lot of attention. More precisely, using pseudo-operational matrices and appropriate approximations based on bivariate Jacobi polynomials, the approximate solutions of the variable-order time-fractional diffusion-type equations in the Caputo sense with high accuracy are formally retrieved. Based on orthogonal bivariate Jacobi polynomials and their operational matrices, a sparse algebraic system is generated which makes implementing the proposed approach easy. An error bound is computed for the residual function by proving some theorems. To illustrate the accuracy and efficiency of the scheme, several illustrative examples are considered. The results demonstrate the efficiency of the present method compared to those achieved by the Legendre and Lucas multi-wavelet methods and the Crank-Nicolson compact method.
Citation Count: Sadri, Khadijeh...et al. (2021). "Bivariate Chebyshev polynomials of the fifth kind for variable-order time-fractional partial integro-differential equations with weakly singular kernel", Advances in Difference Equations, Vol. 2021, No. 1.
Bivariate Chebyshev polynomials of the fifth kind for variable-order time-fractional partial integro-differential equations with weakly singular kernel
(2021) Sadri, Khadijeh; Hosseini, Kamyar; Baleanu, Dumitru; Ahmadian, Ali; Salahshour, Soheil; 56389
The 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.
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: 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.