Browsing by Author "Salahshour, Soheil"

Now showing 1 - 20 of 25

Citation - WoS: 0
Citation - Scopus: 0
A 6-point subdivision scheme and its applications for the solution of 2nd order nonlinear singularly perturbed boundary value problems
(Amer inst Mathematical Sciences-aims, 2020) Mustafa, Ghulam; Baleanu, Dumitru; Baleanu, Dumitru; Ejaz, Syeda Tehmina; Anju, Kaweeta; Ahmadian, Ali; Salahshour, Soheil; Ferrara, Massimiliano; 56389; Matematik
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 - WoS: 93
Citation - Scopus: 113
A Jacobi Operational Matrix for Solving A Fuzzy Linear Fractional Differential Equation
(Springer international Publishing Ag, 2013) Ahmadian, Ali; Baleanu, Dumitru; Suleiman, Mohamed; Salahshour, Soheil; Baleanu, Dumitru; 56389; Matematik
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 - WoS: 37
A new fractional derivative for differential equation of fractional order under interval uncertainty
(Sage Publications Ltd, 2015) Salahshour, Soheil; Baleanu, Dumitru; Ahmadian, Ali; Ismail, Fudzial; Baleanu, Dumitru; Senu, Norazak; Matematik
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 - WoS: 5
Citation - Scopus: 8
A novel weak fuzzy solution for fuzzy linear system
(Mdpi Ag, 2016) Salahshour, Soheil; Baleanu, Dumitru; Ahmadian, Ali; Ismail, Fudziah; Baleanu, Dumitru; Matematik
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.
A novelweak fuzzy solution for fuzzy linear system
(2016) Baleanu, Dumitru; Ahmadian, Ali; Ismail, Fudziah; Baleanu, Dumitru; 56389; Matematik
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 - WoS: 18
Citation - Scopus: 21
A pseudo-operational collocation method for variable-order time-space fractional KdV-Burgers-Kuramoto equation
(Wiley, 2023) Sadri, Khadijeh; Baleanu, Dumitru; Hosseini, Kamyar; Hincal, Evren; Baleanu, Dumitru; Salahshour, Soheil; 56389; Matematik
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 - WoS: 11
Citation - Scopus: 14
A robust scheme for Caputo variable-order time-fractional diffusion-type equations
(Springer, 2023) Sadri, Khadijeh; Baleanu, Dumitru; Hosseini, Kamyar; Baleanu, Dumitru; Salahshour, Soheil; Hincal, Evren; 56389; Matematik
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 - WoS: 36
Citation - Scopus: 43
An effective computational method to deal with a time-fractional nonlinear water wave equation in the Caputo sense
(Elsevier, 2021) Hosseini, Kamyar; Baleanu, Dumitru; Ilie, Mousa; Mirzazadeh, Mohammad; Yusuf, Abdullahi; Sulaiman, Tukur Abdulkadir; Baleanu, Dumitru; Salahshour, Soheil; 56389; Matematik
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 - WoS: 56
Citation - Scopus: 71
An efficient computational approach for local fractional Poisson equation in fractal media
(Wiley, 2021) Singh, Jagdev; Baleanu, Dumitru; Ahmadian, Ali; Rathore, Sushila; Kumar, Devendra; Baleanu, Dumitru; Salimi, Mehdi; Salahshour, Soheil; 56389; Matematik
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 - WoS: 0
Citation - Scopus: 0
An efficient numerical simulation for solving dynamical systems with uncertainty
(Asme, 2017) Ahmadian, Ali; Baleanu, Dumitru; Salahshour, Soheil; Chan, Chee Seng; Baleanu, Dumitur; Matematik
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 - WoS: 11
Citation - Scopus: 17
Bivariate Chebyshev polynomials of the fifth kind for variable-order time-fractional partial integro-differential equations with weakly singular kernel
(Springer, 2021) Sadri, Khadijeh; Baleanu, Dumitru; Hosseini, Kamyar; Baleanu, Dumitru; Ahmadian, Ali; Salahshour, Soheil; 56389; Matematik
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 - WoS: 12
Citation - Scopus: 12
Designing a matrix collocation method for fractional delay integro-differential equations with weakly singular kernels based on vieta–fibonacci polynomials
(Mdpi, 2022) Sadri, Khadijeh; Baleanu, Dumitru; Hosseini, Kamyar; Baleanu, Dumitru; Salahshour, Soheil; Park, Choonkil; 56389; Matematik
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 - WoS: 26
Extension of the fractional derivative operator of the Riemann-Liouville
(int Scientific Research Publications, 2017) Baleanu, Dumitru; Baleanu, Dumitru; Agarwal, Praveen; Parmar, Rakesh K.; Alqurashi, Maysaa M.; Salahshour, Soheil; 56389; Matematik
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 - WoS: 2
Citation - Scopus: 3
Fractional and Time-Scales Differential Equations
(Hindawi Publishing Corporation, 2014) Baleanu, Dumitru; Baleanu, Dumitru; Bhrawy, Ali H.; Torres, Delfim F. M.; Salahshour, Soheil; 56389; Matematik
Citation - WoS: 0
Citation - Scopus: 6
Fuzzy Fractional Ostrowski inequality with Caputo differentiability
(Springer, 2013) Allahviranloo, Tofigh; Baleanu, Dumitru; Avazpour, Lutfi; Ebadi, Mohammad J.; Baleanu, Dumitru; Salahshour, Soheil; 56389; Matematik
Citation - WoS: 9
Citation - Scopus: 11
A High-Accuracy Vieta-Fibonacci Collocation Scheme To Solve Linear Time-Fractional Telegraph Equations
(Taylor & Francis Ltd, 2022) Baleanu, Dumitru; Hosseini, Kamyar; Baleanu, Dumitru; Salahshour, Soheil; Matematik
The vital target of the current work is to construct two-variable Vieta-Fibonacci polynomials which are coupled with a matrix collocation method to solve the time-fractional telegraph equations. The emerged fractional derivative operators in these equations are in the Caputo sense. Telegraph equations arise in the fields of thermodynamics, hydrology, signal analysis, and diffusion process of chemicals. The orthogonality of derivatives of shifted Vieta-Fibonacci polynomials is proved. A bound of the approximation error is ascertained in a Vieta-Fibonacci-weighted Sobolev space that admits increasing the number of terms of the series solution leads to the decrease of the approximation error. The proposed scheme is implemented on four illustrated examples and obtained numerical results are compared with those reported in some existing research works.
Citation - WoS: 52
Citation - Scopus: 61
Numerical Solutions of Fuzzy Differential Equations By an Efficient Runge-Kutta Method With Generalized Differentiability
(Elsevier, 2018) Ahmadian, Ali; Baleanu, Dumitru; Salahshour, Soheil; Chan, Chee Seng; Baleanu, Dumitru; 56389; Matematik
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 - WoS: 132
Citation - Scopus: 150
On analytical solutions of the fractional differential equation with uncertainty: application to the basset problem
(Mdpi, 2015) Salahshour, Soheil; Baleanu, Dumitru; Ahmadian, Ali; Senu, Norazak; Baleanu, Dumitru; Agarwal, Praveen; Matematik
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 - WoS: 5
Citation - Scopus: 1
Retracted: Retracted: Fuzzy Fractional Ostrowski Inequality With Caputo Differentiability (Retracted Article. See 2013)
(Springeropen, 2013) Baleanu, Dumitru; Avazpour, Lutfi; Ebadi, Mohammad J.; Baleanu, Dumitru; Salahshour, Soheil; Matematik
The use of fractional inequalities in mathematical models is increasingly widespread in recent years. In this manuscript, we firstly propose the right Caputo derivative of fuzzy-valued functions about fractional order v (0 < v < 1). To this end, we consider two types of differentiability (similar to the non-fractional case). Then we derive the equivalent integral forms of original fuzzy fractional differential equations. Finally, we prove the fuzzy Ostrowski inequality involving three functions under Caputo's differentiability. In this regard, we state some new results.
Citation - WoS: 76
Citation - Scopus: 79
The (2 + 1)-dimensional Heisenberg ferromagnetic spin chain equation: its solitons and Jacobi elliptic function solutions
(Springer Heidelberg, 2021) Hosseini, Kamyar; Baleanu, Dumitru; Salahshour, Soheil; Mirzazadeh, Mohammad; Ahmadian, Ali; Baleanu, Dumitru; Khoshrang, Arian; 56389; Matematik
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.