Browsing by Author "Salahshour, S."

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Citation Count: Salahshour, S...et al. "A fractional derivative with non-singular kernel for interval-valued functions under uncertainty", Optik, Vol. 130, pp. 273-286.
A fractional derivative with non-singular kernel for interval-valued functions under uncertainty
(Elsevier GMBH, 2017) Salahshour, S.; Ahmadian, Ali; İsmail, F.; Baleanu, Dumitru; 56389
The purpose of the current investigation is to generalize the concept of fractional derivative in the sense of Caputo Fabrizio derivative (CF-derivative) for interval-valued function under uncertainty. The reason to choose this new approach is originated from the non singularity property of the kernel that is critical to interpret the memory aftermath of the system, which was not precisely illustrated in the previous definitions. We study the properties of CF-derivative for interval-valued functions under generalized Hukuhara-differentiability. Then, the fractional differential equations under this notion are presented in details. We also study three real-world systems such as the falling body problem, Basset and Decay problem under interval-valued CF-differentiability. Our cases involve a demonstration that this new notion is accurately applicable for the mechanical and viscoelastic models based on the interval CF-derivative equations.
Citation Count: Hosseini, K.;...et.al. "A new generalized KdV equation: Its lump-type, complexiton and soliton solutions", International Journal of Modern Physics B, Vol.36, No.31.
A new generalized KdV equation: Its lump-type, complexiton and soliton solutions
(2022) Hosseini, K.; Salahshour, S.; Baleanu, D.; Mirzazadeh, M.; Dehingia, K.; 56389
A new generalized KdV equation, describing the motions of long waves in shallow water under the gravity field, is considered in this paper. By adopting a series of well-organized methods, the Bäcklund transformation, the bilinear form and diverse wave structures of the governing model are formally extracted. The exact solutions listed in this paper are categorized as lump-type, complexiton, and soliton solutions. To exhibit the physical mechanism of the obtained solutions, several graphical illustrations are given for particular choices of the involved parameters. As a direct consequence, diverse wave structures given in this paper enrich the studies on the KdV-type equations.
Citation Count: Karimi Dizicheh, A...et al. (2020). "A Novel Algorithm Based On the Legendre Wavelets Spectral Technique for Solving the Lane–Emden Equations", Applied Numerical Mathematics, Vol. 153, pp.443-456.
A Novel Algorithm Based On the Legendre Wavelets Spectral Technique for Solving the Lane–Emden Equations
(Elsevier B.V., 2020) Karimi Dizicheh, A.; Salahshour, S.; Ahmadian, Ali; Baleanu, Dumitru; 56389
In this research, we present an iterative spectral method for the approximate solution of a class of Lane–Emden equations. In this procedure, we initially extend the Legendre wavelet which is appropriate for any time interval. Thereafter, the Guass-Legendre collection points of the Legendre wavelet are acquired. Employing this new approach, the iterative spectral technique converts the differential equation to a set of algebraic equations which diminishes the computational costs effectively. By solving the obtained algebraic equations, an accurate approximate solution for the assumed Lane–Emden equation is achieved. The present technique is validated by solving a number of Lane–Emden problems and are compared with other existing methods. The numerical simulations demonstrate that the new algorithm is simple and it has highly accuracy.
Citation Count: Ahmadian, A...et al. (2017). A novel approach to approximate fractional derivative with uncertain conditions Chaos Solitons & Fractals, 104, 68-76 .
A novel approach to approximate fractional derivative with uncertain conditions
(Elsevier, 2017) Ahmadian, Ali; Salahshour, S.; Ali-Akbari, Mahdi; İsmail, F.; Baleanu, Dumitru; 56389
This paper focuses on providing a new scheme to find the fuzzy approximate solution of fractional differential equations (FDEs) under uncertainty. The Caputo-type derivative base on the generalized Hukuhara differentiability is approximated by a linearization formula to reduce the corresponding uncertain FDE to an ODE under fuzzy concept. This new approach may positively affect on the computational cost and easily apply for the other types of uncertain fractional-order differential equation. The performed numerical simulations verify the proficiency of the presented scheme
Citation Count: Bishehniasar, M...et al. (2017). An Accurate Approximate-Analytical Technique for Solving Time-Fractional Partial Differential Equations, Complexity.
An Accurate Approximate-Analytical Technique for Solving Time-Fractional Partial Differential Equations
(Wiley-Hindawi, 2017) Bishehniasar, M.; Salahshour, S.; Ahmadian, Ali; İsmail, F.; Baleanu, Dumitru; 56389
The demand of many scientific areas for the usage of fractional partial differential equations (FPDEs) to explain their real-world systems has been broadly identified. The solutions may portray dynamical behaviors of various particles such as chemicals and cells. The desire of obtaining approximate solutions to treat these equations aims to overcome the mathematical complexity of modeling the relevant phenomena in nature. This research proposes a promising approximate-analytical scheme that is an accurate technique for solving a variety of noninteger partial differential equations (PDEs). The proposed strategy is based on approximating the derivative of fractional-order and reducing the problem to the corresponding partial differential equation (PDE). Afterwards, the approximating PDE is solved by using a separation-variables technique. The method can be simply applied to nonhomogeneous problems and is proficient to diminish the span of computational cost as well as achieving an approximate-analytical solution that is in excellent concurrence with the exact solution of the original problem. In addition and to demonstrate the efficiency of the method, it compares with two finite difference methods including a nonstandard finite difference (NSFD) method and standard finite difference (SFD) technique, which are popular in the literature for solving engineering problems.
Citation Count: Salahshour, S...et al. (2019). "Asymptotic solutions of fractional interval differential equations with nonsingular kernel derivative", Chaos, Vol. 29, No. 8.
Asymptotic solutions of fractional interval differential equations with nonsingular kernel derivative
(Amer Inst Physics, 2019) Salahshour, S.; Ahmadian, Ali; Salimi, M.; Ferrara, M.; Baleanu, Dumitru; 56389
Realizing the behavior of the solution in the asymptotic situations is essential for repetitive applications in the control theory and modeling of the real-world systems. This study discusses a robust and definitive attitude to find the interval approximate asymptotic solutions of fractional differential equations (FDEs) with the Atangana-Baleanu (A-B) derivative. In fact, such critical tasks require to observe precisely the behavior of the noninterval case at first. In this regard, we initially shed light on the noninterval cases and analyze the behavior of the approximate asymptotic solutions, and then, we introduce the A-B derivative for FDEs under interval arithmetic and develop a new and reliable approximation approach for fractional interval differential equations with the interval A-B derivative to get the interval approximate asymptotic solutions. We exploit Laplace transforms to get the asymptotic approximate solution based on the interval asymptotic A-B fractional derivatives under interval arithmetic. The techniques developed here provide essential tools for finding interval approximation asymptotic solutions under interval fractional derivatives with nonsingular Mittag-Leffler kernels. Two cases arising in the real-world systems are modeled under interval notion and given to interpret the behavior of the interval approximate asymptotic solutions under different conditions as well as to validate this new approach. This study highlights the importance of the asymptotic solutions for FDEs regardless of interval or noninterval parameters. Published under license by AIP Publishing.
Citation Count: Hosseini K.;...et.al. (2023). "Bäcklund Transformation, Complexiton, and Solitons of a (4 + 1)-dimensional Nonlinear Evolutionary Equation", International Journal of Applied and Computational Mathematics, Vol.8, No.6.
Bäcklund Transformation, Complexiton, and Solitons of a (4 + 1)-dimensional Nonlinear Evolutionary Equation
(2022) Hosseini, K.; Salahshour, S.; Baleanu, D.; Mirzazadeh, M.; 56389
The main purpose of the current paper is to establish a (4 + 1)-dimensional nonlinear evolutionary (4D-NLE) equation and derive its Bäcklund transformation, complexiton, and solitons. To this end, the Bäcklund transformation of the 4D-NLE equation is first constructed by applying the truncated Painlevé expansion. The simplified Hirota’s method is then employed to acquire the solitons of the governing model. In the end, the complexiton of the 4D-NLE equation is retrieved using the Zhou–Ma method. As the completion of studies, several graphical representations are considered for different parameter values to show the dynamics of complexiton and solitons.
Citation Count: Salahshour, S...et al. (2012). "Existence and uniqueness results for fractional differential equations with uncertainty", Advances In Difference Equations.
Existence and Uniqueness Results for Fractional Differential Equations With Uncertainty
(Springer International Publishing AG, 2012) Salahshour, S.; Allahviranloo, Tofigh; Abbasbandy, S.; Baleanu, Dumitru; 56389
In this paper, we study the existence, uniqueness and approximate solutions of fuzzy fractional differential equations (FFDEs) under Caputo's H-differentiability. To this end, the concept of Riemann-Liouville's H-differentiability is introduced, and subsequently, the Caputo's H-differentiability is proposed. Moreover, the related fuzzy Volterra integral forms of FFDEs are obtained which are applied to construct two converge consequences of fuzzy-valued functions as approximated solutions of FFDEs.
Citation Count: Khoshkenar, A. (2022). "Further studies on ordinary differential equations involving the M-fractional derivative", AIMS Mathematics, Vol.7, No.6, pp.10977-10993.
Further studies on ordinary differential equations involving the M-fractional derivative
(2022) Khoshkenar, A.; Ilie, M.; Hosseini, K.; Baleanu, D.; Salahshour, S.; Park, C.; Lee, J.R.; 56389
In the current paper, the power series based on the M-fractional derivative is formally introduced. More peciesely, the Taylor and Maclaurin expansions are generalized for fractional-order differentiable functions in accordance with the M-fractional derivative. Some new definitions, theorems, and corollaries regarding the power series in the M sense are presented and formally proved. Several ordinary differential equations (ODEs) involving the M-fractional derivative are solved to examine the validity of the results presented in the current study.
Citation Count: Allahviranloo, T...et al. (2018). "General Solutions of Fully Fuzzy Linear Systems", Abstract and Applied Analysis.
General Solutions of Fully Fuzzy Linear Systems
(Hindawi LTD, 2013) Allahviranloo, Tofigh; Salahshour, S.; Homayoun-nejad, M.; Baleanu, Dumitru; 56389
We propose a method to approximate the solutions of fully fuzzy linear system (FFLS), the so-called general solutions. So, we firstly solve the 1-cut position of a system, then some unknown spreads are allocated to each row of an FFLS. Using this methodology, we obtain some general solutions which are placed in the well-known solution sets like Tolerable solution set (TSS) and Controllable solution set (CSS). Finally, we solved two examples in order to demonstrate the ability of the proposed method.
Citation Count: Salahshour, S.; Ahmadian, A.; Abbasbandy, S.; et al., "M-fractional derivative under interval uncertainty: Theory, properties and applications", Chaos Solitons & Fractals, Vol. 117, pp. 84-93, (2018).
M-fractional derivative under interval uncertainty: Theory, properties and applications
(Pergamon-Elsevier Science LTD, 2018) Salahshour, S.; Ahmadian, Ali; Abbasbandy, S.; Baleanu, Dumitru; 56389
In the recent years some efforts were made to propose simple and well-behaved fractional derivatives that inherit the classical properties from the first order derivative. In this regards, the truncated M-fractional derivative for alpha-differentiable function was recently introduced that is a generalization of four fractional derivatives presented in the literature and has their important features. In this research, we aim to generalize this novel and effective derivative under interval uncertainty. The concept of interval truncated M-fractional derivative is introduced and some of the distinguished properties of this interesting fractional derivative such as Rolle's and mean value theorems, are developed for the interval functions. In addition, the existence and uniqueness conditions of the solution for the interval fractional differential equations (IFDEs) based on this new derivative are also investigated. Finally, we present the applicability of this novel interval fractional derivative for IFDEs based on the notion of w-increasing (w-decreasing) by solving a number of test problems. (C) 2018 Elsevier Ltd. All rights reserved.
Citation Count: Hosseini K.,...et.al. (2022). "Multi-complexiton and positive multi-complexiton structures to a generalized B-type Kadomtsev−Petviashvili equation", Journal of Ocean Engineering and Science.
Multi-complexiton and positive multi-complexiton structures to a generalized B-type Kadomtsev−Petviashvili equation
(2022) Hosseini, K.; Baleanu, D.; Rezapour, S.; Salahshour, S.; Mirzazadeh, M.; Samavat, M.; 56389
Recently, Zhang et al. (International Journal of Modern Physics B 30 (2016) 1640029) constructed N-wave solutions of a generalized B-type Kadomtsev−Petviashvili (gbKP) equation using the linear superposition method. The authors’ aim of the present paper is to derive multi-complexiton and positive multi-complexiton structures of the gbKP equation through considering N-wave solutions and applying specific systematic methods. To investigate the dynamical characteristics of positive multi-complexiton structures, particularly single and double positive complexitons, several two and three-dimensional simulations are formally considered. The results of the current research enrich the studies regarding the gbKP equation.
Citation Count: Hosseini K.;...et.al. (2023). "Non-singular multi-complexiton wave to a generalized KdV equation", Nonlinear Dynamics, Vol.111, No.8, pp.7591-7597.
Non-singular multi-complexiton wave to a generalized KdV equation
(2023) Hosseini, K.; Hıncal, E.; Baleanu, D.; Obi, O.A.; Salahshour, S.; 56389
The major goal of the current paper is to conduct a detailed study on a generalized KdV equation (gKdVE) and its non-singular multi-complexiton wave. More precisely, first the multi-shock wave of the governing model is retrieved using the principle of linear superposition. Based on the multi-shock wave and the techniques adopted by Zhou and Manukure, the non-singular multi-complexiton wave to the gKdVE is then constructed with the help of symbolic computations. The dynamical properties of single and double shock waves as well as non-singular single and double complexiton waves are analyzed by representing a group of 3D-plots. The achievements of the present paper take an important step in completing the research on the generalized KdV equation.
Citation Count: Allahviranloo, T...et al. (2013). "On Solutions of Linear Fractional Differential Equations with Uncertainty", Abstract and Applied Analysis.
On Solutions of Linear Fractional Differential Equations With Uncertainty
(Hindawi LTD, 2013) Allahviranloo, Tofigh; Abbasbandy, S.; Shahryari, M. R. Balooch; Salahshour, S.; Baleanu, Dumitru; 56389
The solutions of linear fuzzy fractional differential equations (FFDEs) under the Caputo differentiability have been investigated. To this end, the fuzzy Laplace transform was used to obtain the solutions of FFDEs. Then, some new results regarding the relation between some types of differentiability have been obtained. Finally, some applicable examples are solved in order to show the ability of the proposed method.
Citation Count: Hosseini K.;...et.al. (2022). "Optical solitons of a high-order nonlinear Schrödinger equation involving nonlinear dispersions and Kerr effect", Optical and Quantum Electronics, Vol.54, no.3.
Optical solitons of a high-order nonlinear Schrödinger equation involving nonlinear dispersions and Kerr effect
(2022) Hosseini, K.; Mirzazadeh, M.; Baleanu, D.; Salahshour, S.; Akinyemi, L.; 56389
The main aim of this paper is to conduct a detailed study on a high-order nonlinear Schrödinger (HONLS) equation involving nonlinear dispersions and the Kerr effect. More precisely, after reducing the governing model describing ultra-short pulses in optical fibers in a one-dimensional domain, its optical solitons including the bright and dark solitons are derived through the modified Kudryashov (MK) method. The dynamical behavior of the bright and dark solitons is formally investigated for different sets of the involved parameters. It is shown that increasing and decreasing nonlinear dispersions lead to significant changes in the amplitude of the bright and dark solitons.
Citation Count: Hosseini K.;...et.al. (2022). "Optical solitons to the Ginzburg–Landau equation including the parabolic nonlinearity", Optical and Quantum Electronics, Vol.54, No.10.
Optical solitons to the Ginzburg–Landau equation including the parabolic nonlinearity
(2022) Hosseini, K.; Mirzazadeh, M.; Akinyemi, L.; Baleanu, D.; Salahshour, S.; 56389
The major goal of the present paper is to construct optical solitons of the Ginzburg–Landau equation including the parabolic nonlinearity. Such an ultimate goal is formally achieved with the aid of symbolic computation, a complex transformation, and Kudryashov and exponential methods. Several numerical simulations are given to explore the influence of the coefficients of nonlinear terms on the dynamical features of the obtained optical solitons. To the best of the authors’ knowledge, the results reported in the current study, classified as bright and kink solitons, have a significant role in completing studies on the Ginzburg–Landau equation including the parabolic nonlinearity.
Citation Count: Hosseini K.;...et.al. (2023). "Periodic and solitary waves of the nonlinear Konno–Oono model: generalized methods", Optical and Quantum Electronics, Vol.55, No.6.
Periodic and solitary waves of the nonlinear Konno–Oono model: generalized methods
(2023) Hosseini, K.; Sadri, K.; Hıncal, E.; Abbasi, A.; Baleanu, D.; Salahshour, S.; 56389
There has been considerable academic interest in the study of nonlinear dynamical models and their exact traveling waves over the past few years. The main aim of the present paper is to consider a nonlinear dynamical model known as the nonlinear Konno–Oono model and derive its exact traveling waves. Specifically, after applying a universal transformation, periodic and solitary waves of the governing model with applications in the electromagnetic field are derived using generalized methods. Through the consideration of two- and three-dimensional simulations, several case studies are considered to represent the dynamical behavior of soliton solutions.
Citation Count: Madhukalya B.;...et.al. (2023). "Small amplitude ion-acoustic solitary waves in a magnetized ion-beam plasma under the effect of ion and beam temperatures", European Physical Journal Plus, Vol.138, No.4.
Small amplitude ion-acoustic solitary waves in a magnetized ion-beam plasma under the effect of ion and beam temperatures
(2023) Madhukalya, B.; Das, R.; Hosseini, K.; Baleanu, D.; Salahshour, S.; 56389
In the present research of magnetized plasmas, both rarefactive and compressive solitons are found to exist, based on the values of certain parameters. It has been shown in the present investigation that inclusion of beam temperature into the plasma is in search of the existence of both slow and fast modes for both the cases Q′< 1 and Q′> 1. Furthermore, it is noteworthy to point out that the ion-acoustic soliton is found to exist for γ=UdsinθM=beam velocityphase velocity=1 as well. © 2023, The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature.
Citation Count: Salahshour, S...et al. (2021). "Soliton structures of a nonlinear Schrödinger equation involving the parabolic law", Optical and Quantum Electronics, Vol. 53, No. 12.
Soliton structures of a nonlinear Schrödinger equation involving the parabolic law
(2021) Salahshour, S.; Hosseini, K.; Mirzazadeh, M.; Baleanu, Dumitru; 56389
The search for soliton structures plays a pivotal role in many scientific disciplines particularly in nonlinear optics. The main concern of the present paper is to explore the dynamics of soliton structures in a nonlinear Schrödinger (NLS) equation with the parabolic law. In this respect, the reduced form of the NLS equation is firstly extracted; then, its soliton structures are derived in the presence of spatio-temporal dispersions using the Kudryashov method. As the completion of studies, the impact of increasing and decreasing the coefficients of the parabolic law on the dynamics of soliton structures is formally addressed through representing several two- and three-dimensional figures.
Citation Count: Kalita J.;...et.al. (2023). "Solitons in magnetized plasma with electron inertia under weakly relativistic effect", Nonlinear Dynamics, Vol.111, No.4, ppç3701-3711.
Solitons in magnetized plasma with electron inertia under weakly relativistic effect
(2023) Kalita, J.; Das, R.; Hosseini, K.; Baleanu, Dumitru; Salahshour, S.; 56389
In this relativistic consideration, the energy integral unlike others has been derived in a weakly relativistic plasma in terms of Sagdeev potential. Both compressive and rarefactive subsonic solitary waves are found to exist, depending on wave speeds in various directions of propagation. It is found that compressive relativistic solitons have potential depths that are higher than non-relativistic solitons in all directions of propagation, allowing for the presence of denser plasma particles in the potential well. Furthermore, it shows how compressive soliton amplitude grows as the propagation direction gets closer to the magnetic field’s direction.