Browsing by Author "Salahshour, Soheil"

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Citation Count: Mustafa, Ghulam...et al. (2020). "A 6-point subdivision scheme and its applications for the solution of 2nd order nonlinear singularly perturbed boundary value problems", Mathematical Biosciences and Engineering, Vol. 17, No. 6, pp. 6659-6677.
A 6-point subdivision scheme and its applications for the solution of 2nd order nonlinear singularly perturbed boundary value problems
(2020) Mustafa, Ghulam; Baleanu, Dumitru; Ejaz, Syeda Tehmina; Anju, Kaweeta; Ahmadian, Ali; Salahshour, Soheil; Ferrara, Massimiliano; 56389
In this paper, we first present a 6-point binary interpolating subdivision scheme (BISS) which produces a C 2 continuous curve and 4th order of approximation. Then as an application of the scheme, we develop an iterative algorithm for the solution of 2nd order nonlinear singularly perturbed boundary value problems (NSPBVP). The convergence of an iterative algorithm has also been presented. The 2nd order NSPBVP arising from combustion, chemical reactor theory, nuclear engineering, control theory, elasticity, and fluid mechanics can be solved by an iterative algorithm with 4th order of approximation.
Citation Count: Dehingia, Kaushik...et.al. (2022). "A Detailed Study on a Tumor Model with Delayed Growth of Pro-Tumor Macrophages", International Journal of Applied and Computational Mathematics, Vol.8, No.5
A Detailed Study on a Tumor Model with Delayed Growth of Pro-Tumor Macrophages
(2022) Dehingia, Kaushik; Hosseini, Kamyar; Salahshour, Soheil; Baleanu, D.; 56389
This paper investigates a tumor-macrophages interaction model with a discrete-time delay in the growth of pro-tumor M2 macrophages. The steady-state analysis of the governing model is performed around the tumor dominant steady-state and the interior steady-state. It is found that the tumor dominant steady-state is locally asymptotically stable under certain conditions, and the stability of the interior steady-state is affected by the discrete-time delay; as a result, the unstable system experiences a Hopf bifurcation and gets stabilized. Furthermore, the transversality conditions for the existence of Hopf bifurcations are derived. Several graphical representations in two and three-dimensional postures are given to examine the validity of the results provided in the current study.
Citation Count: Ahmadian, Ali...et al. (20139. "A Jacobi operational matrix for solving a fuzzy linear fractional differential equation", Advances In Difference Equations.
A Jacobi Operational Matrix for Solving A Fuzzy Linear Fractional Differential Equation
(Springer International Publishing AG, 2013) Ahmadian, Ali; Suleiman, Mohamed; Salahshour, Soheil; Baleanu, Dumitru; 56389
This paper reveals a computational method based using a tau method with Jacobi polynomials for the solution of fuzzy linear fractional differential equations of order . A suitable representation of the fuzzy solution via Jacobi polynomials diminishes its numerical results to the solution of a system of algebraic equations. The main advantage of this method is its high robustness and accuracy gained by a small number of Jacobi functions. The efficiency and applicability of the proposed method are proved by several test examples.
Citation Count: Samavat, Majid;...et.al. (2022). "A New (4 + 1)-Dimensional Burgers Equation: Its Bäcklund Transformation and Real and Complex -Kink Solitons", International Journal of Applied and Computational Mathematics, Vol.8, No.172.
A New (4 + 1)-Dimensional Burgers Equation: Its Bäcklund Transformation and Real and Complex -Kink Solitons
(2022) Samavat, Majid; Mirzazadeh, Mohammad; Hosseini, Kamyar; Salahshour, Soheil; Baleanu, Dumitru; 56389
Studying the dynamics of solitons in nonlinear evolution equations (NLEEs) has gainedconsiderable interest in the last decades. Accordingly, the search for soliton solutions ofNLEEs has been the main topic of many research studies. In the present paper, a new (4+ 1)-dimensional Burgers equation (n4D-BE) is introduced that describes speciﬁc disper-sive waves in nonlinear sciences. Based on the truncated Painlevé expansion, the Bäcklundtransformation of the n4D-BE is ﬁrstly extracted, then, its real and complex N-kink solitonsare derived using the simpliﬁed Hirota method. Furthermore, several ansatz methods areformally adopted to obtain a group of other single-kink soliton solutions of the n4D-BE
Citation Count: Salahshour, S...et al. (2015). A new fractional derivative for differential equation of fractional order under interval uncertainty. Advance In Mechanical Engineering, 7(12). http://dx.doi.org/10.1177/1687814015619138
A new fractional derivative for differential equation of fractional order under interval uncertainty
(Sage Publications LTD, 2015) Salahshour, Soheil; Ahmadian, Ali; Ismail, Fudziah; Baleanu, Dumitru; Senu, Norazak
In this article, we develop a new definition of fractional derivative under interval uncertainty. This fractional derivative, which is called conformable fractional derivative, inherits some interesting properties from the integer differentiability which is more convenient to work with the mathematical models of the real-world phenomena. The interest for this new approach was born from the notion that makes a dependency just on the basic limit definition of the derivative. We will introduce and prove the main features of this well-behaved simple fractional derivative under interval arithmetic uncertainty. The actualization and usefulness of this approach are validated by solving two practical models
Citation Count: Salahshour, S...et al. (2015). A novel weak fuzzy solution for fuzzy linear system. Entropy, 18(3). http://dx.doi.org/10.3390/e18030068
A novel weak fuzzy solution for fuzzy linear system
(MDPI AG, 2016) Salahshour, Soheil; Ahmadian, Ali; Ismail, Fudziah; Baleanu, Dumitru
This article proposes a novel weak fuzzy solution for the fuzzy linear system. As a matter of fact, we define the right-hand side column of the fuzzy linear system as a piecewise fuzzy function to overcome the related shortcoming, which exists in the previous findings. The strong point of this proposal is that the weak fuzzy solution is always a fuzzy number vector. Two complex and non-complex linear systems under uncertainty are tested to validate the effectiveness and correctness of the presented method
Citation Count: Salahshour, Soheil;...et.al. (2016). "A novelweak fuzzy solution for fuzzy linear system", Entropy, Vol.18, No.3.
A novelweak fuzzy solution for fuzzy linear system
(2016) Salahshour, Soheil; Ahmadian, Ali; Ismail, Fudziah; Baleanu, Dumitru; 56389
This article proposes a novel weak fuzzy solution for the fuzzy linear system. As a matter of fact, we define the right-hand side column of the fuzzy linear system as a piecewise fuzzy function to overcome the related shortcoming, which exists in the previous findings. The strong point of this proposal is that the weak fuzzy solution is always a fuzzy number vector. Two complex and non-complex linear systems under uncertainty are tested to validate the effectiveness and correctness of the presented method.
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: Hosseini, Kamyar...et al. (20219. "An effective computational method to deal with a time-fractional nonlinear water wave equation in the Caputo sense", Mathematics and Computers in Simulation, Vol. 187, pp. 248-260.
An effective computational method to deal with a time-fractional nonlinear water wave equation in the Caputo sense
(2021) Hosseini, Kamyar; Ilie, Mousa; Mirzazadeh, Mohammad; Yusuf, Abdullahi; Sulaiman, Tukur Abdulkadi; Baleanu, Dumitru; Salahshour, Soheil; 56389
The authors' concern of the present paper is to conduct a systematic study on a time-fractional nonlinear water wave equation which is an evolutionary version of the Boussinesq system. The study goes on by adopting a new analytical method based on the Laplace transform and the homotopy analysis method to the governing model and obtaining its approximate solutions in the presence of the Caputo fractional derivative. To analyze the influence of the Caputo operator on the dynamical behavior of the approximate solutions, some graphical illustrations in two- and three-dimensions are formally presented. Furthermore, several numerical tables are given to support the performance of the new analytical method in handling the time-fractional nonlinear water wave equation. (C) 2021 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.
Citation Count: Singh, Jagdev...et al. (2021). "An efficient computational approach for local fractional Poisson equation in fractal media", Numerical Methods for Partial Differential Equations, Vol. 37, No. 2, pp. 1439-1448.
An efficient computational approach for local fractional Poisson equation in fractal media
(2021) Singh, Jagdev; Ahmadian, Ali; Rathore, Sushila; Kumar, Devendra; Baleanu, Dumitru; Salimi, Mehdi; Salahshour, Soheil; 56389
In this article, we analyze local fractional Poisson equation (LFPE) by employing q-homotopy analysis transform method (q-HATM). The PE describes the potential field due to a given charge with the potential field known, one can then calculate gravitational or electrostatic field in fractal domain. It is an elliptic partial differential equations (PDE) that regularly appear in the modeling of the electromagnetic mechanism. In this work, PE is studied in the local fractional operator sense. To handle the LFPE some illustrative example is discussed. The required results are presented to demonstrate the simple and well-organized nature of q-HATM to handle PDE having fractional derivative in local fractional operator sense. The results derived by the discussed technique reveal that the suggested scheme is easy to employ and computationally very accurate. The graphical representation of solution of LFPE yields interesting and better physical consequences of Poisson equation with local fractional derivative.
Citation Count: Ahmadian, A...et al. (2017). An efficient numerical simulation for solving dynamical systems with uncertainty. Journal of Computational and Nonlinear Dynamics, 12(5). http://dx.doi.org/ 10.1115/1.4036419
An efficient numerical simulation for solving dynamical systems with uncertainty
(Asme, 2017) Ahmadian, Ali; Salahshour, Soheil; Chan, Chee Seng; Baleanu, Dumitru
In a wide range of real-world physical and dynamical systems, precise defining of the uncertain parameters in their mathematical models is a crucial issue. It is well known that the usage of fuzzy differential equations (FDEs) is a way to exhibit these possibilistic uncertainties. In this research, a fast and accurate type of Runge-Kutta (RK) methods is generalized that are for solving first-order fuzzy dynamical systems. An interesting feature of the structure of this technique is that the data from previous steps are exploited that reduce substantially the computational costs. The major novelty of this research is that we provide the conditions of the stability and convergence of the method in the fuzzy area, which significantly completes the previous findings in the literature. The experimental results demonstrate the robustness of our technique by solving linear and nonlinear uncertain dynamical systems.
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. (2017). Extension of the fractional derivative operator of the Riemann-Liouville, Journal of Nonlinear Sciences And Applications, 10(6), 2914-2924.
Extension of the fractional derivative operator of the Riemann-Liouville
(Int Scientific Research Publications, 2017) Baleanu, Dumitru; Agarwal, Ravi P.; Parmar, Rakesh K.; Alqurashi, Maysaa; Salahshour, Soheil; 56389
By using the generalized beta function, we extend the fractional derivative operator of the Riemann-Liouville and discusses its properties. Moreover, we establish some relations to extended special functions of two and three variables via generating functions. (C) 2017 All rights reserved.
Citation Count: Baleanu, Dumitru...et al. (2014). "Fractional and Time-Scales Differential Equations", Abstract and Applied Analysis.
Fractional and Time-Scales Differential Equations
(Hindawi LTD, 2014) Baleanu, Dumitru; Bhrawy, Ali H.; Torres, Delfim F. M.; Salahshour, Soheil; 56389
Numerical Solutions of Fuzzy Differential Equations By an Efficient Runge-Kutta Method With Generalized Differentiability
(Elsevier, 2018) Ahmadian, Ali; Salahshour, Soheil; Chan, Chee Seng; Baleanu, Dumitru; 56389
In this paper, an extended fourth-order Runge-Kutta method is studied to approximate the solutions of first-order fuzzy differential equations using a generalized characterization theorem. In this method, new parameters are utilized in order to enhance the order of accuracy of the solutions using evaluations of both f and f', instead of using the evaluations of f only. The proposed extended Runge-Kutta method and its error analysis, which guarantees pointwise convergence, are given in detail. Furthermore, the accuracy and efficiency of the proposed method are demonstrated in a series of numerical experiments. (C) 2016 Elsevier B.V. All rights reserved.
Citation Count: Salahshour, S...et al. (2015). On analytical solutions of the fractional differential equation with uncertainty: application to the basset problem. Entropy, 17(2), 885-902. http://dx.doi.org/10.3390/e17020885
On analytical solutions of the fractional differential equation with uncertainty: application to the basset problem
(MDPI AG, 2015) Salahshour, Soheil; Ahmadian, Ali; Senu, Norazak; Baleanu, Dumitru; Agarwal, Ravi P.
In this paper, we apply the concept of Caputo's H-differentiability, constructed based on the generalized Hukuhara difference, to solve the fuzzy fractional differential equation (FFDE) with uncertainty. This is in contrast to conventional solutions that either require a quantity of fractional derivatives of unknown solution at the initial point (Riemann-Liouville) or a solution with increasing length of their support (Hukuhara difference). Then, in order to solve the FFDE analytically, we introduce the fuzzy Laplace transform of the Caputo H-derivative. To the best of our knowledge, there is limited research devoted to the analytical methods to solve the FFDE under the fuzzy Caputo fractional differentiability. An analytical solution is presented to confirm the capability of the proposed method.
Citation Count: Hosseini, Kamyar...et.al. (2021). "The (2 + 1)-dimensional Heisenberg ferromagnetic spin chain equation: its solitons and Jacobi elliptic function solutions", The European Physical Journal Plus, Vol.136, No.2.
The (2 + 1)-dimensional Heisenberg ferromagnetic spin chain equation: its solitons and Jacobi elliptic function solutions
(2021) Hosseini, Kamyar; Salahshour, Soheil; Mirzazadeh, Mohammad; Ahmadian, Ali; Baleanu, Dumitru; Khoshrang, Arian; 56389
The search for exact solutions of nonlinear evolution models with different wave structures has achieved significant attention in recent decades. The present paper studies a nonlinear (2 + 1)-dimensional evolution model describing the propagation of nonlinear waves in Heisenberg ferromagnetic spin chain system. The intended aim is carried out by considering a specific transformation and adopting a modified version of the Jacobi elliptic expansion method. As a result, a number of solitons and Jacobi elliptic function solutions to the Heisenberg ferromagnetic spin chain equation are formally derived. Several three-dimensional plots are presented to demonstrate the dynamical features of the bright and dark soliton solutions.
Citation Count: Hosseini, Kamyar...et al. (2021). "The (2+1)-dimensional Heisenberg ferromagnetic spin chain equation: its solitons and Jacobi elliptic function solutions", European Physical Journal Plus, Vol. 136, No. 2.
The (2+1)-dimensional Heisenberg ferromagnetic spin chain equation: its solitons and Jacobi elliptic function solutions
(2021) Hosseini, Kamyar; Salahshour, Soheil; Mirzazadeh, Mohammad; Ahmadian, Ali; Baleanu, Dumitru; Khoshrang, Arian; 56389
The search for exact solutions of nonlinear evolution models with different wave structures has achieved significant attention in recent decades. The present paper studies a nonlinear (2+1)-dimensional evolution model describing the propagation of nonlinear waves in Heisenberg ferromagnetic spin chain system. The intended aim is carried out by considering a specific transformation and adopting a modified version of the Jacobi elliptic expansion method. As a result, a number of solitons and Jacobi elliptic function solutions to the Heisenberg ferromagnetic spin chain equation are formally derived. Several three-dimensional plots are presented to demonstrate the dynamical features of the bright and dark soliton solutions.
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.