Browsing by Author "Salahshour, S."

Now showing 1 - 20 of 34

Citation - WoS: 14
Citation - Scopus: 16
An Accurate Approximate-Analytical Technique for Solving Time-Fractional Partial Differential Equations
(Wiley-hindawi, 2017) Salahshour, S.; Ahmadian, A.; Ismail, F.; Baleanu, D.; Bishehniasar, M.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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 - WoS: 26
Citation - Scopus: 31
Asymptotic Solutions of Fractional Interval Differential Equations With Nonsingular Kernel Derivative
(Amer inst Physics, 2019) Ahmadian, A.; Salimi, M.; Ferrara, M.; Baleanu, D.; Salahshour, S.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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 - Scopus: 2
Bäcklund Transformation, Complexiton, and Solitons of a (4 + 1)-Dimensional Nonlinear Evolutionary Equation
(Springer, 2022) Hosseini, K.; Salahshour, S.; Baleanu, D.; Mirzazadeh, M.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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. © 2022, The Author(s), under exclusive licence to Springer Nature India Private Limited.
Citation - Scopus: 11
A Detailed Study on a Tumor Model With Delayed Growth of Pro-Tumor Macrophages
(Springer, 2022) Dehingia, K.; Hosseini, K.; Salahshour, S.; Baleanu, D.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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. © 2022, The Author(s), under exclusive licence to Springer Nature India Private Limited.
Citation - WoS: 88
Existence and Uniqueness Results for Fractional Differential Equations With Uncertainty
(Springer, 2012) Allahviranloo, T.; Abbasbandy, S.; Baleanu, D.; Salahshour, S.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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 - WoS: 37
Citation - Scopus: 44
A Fractional Derivative With Non-Singular Kernel for Interval-Valued Functions Under Uncertainty
(Elsevier Gmbh, Urban & Fischer verlag, 2017) Ahmadian, A.; Ismail, F.; Baleanu, D.; Salahshour, S.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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. (C) 2016 Elsevier GmbH. All rights reserved.
Citation - WoS: 3
Citation - Scopus: 4
Further Studies on Ordinary Differential Equations Involving the M-Fractional Derivative
(Amer inst Mathematical Sciences-aims, 2022) Khoshkenar, A.; Ilie, M.; Hosseini, K.; Baleanu, D.; Salahshour, S.; Park, C.; Lee, J. R.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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 - WoS: 10
Citation - Scopus: 18
General Solutions of Fully Fuzzy Linear Systems
(Hindawi Ltd, 2013) Salahshour, S.; Homayoun-nejad, M.; Baleanu, D.; Allahviranloo, T.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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 - WoS: 31
Citation - Scopus: 40
The Generalized Complex Ginzburg-Landau Model and Its Dark and Bright Soliton Solutions
(Springer Heidelberg, 2021) Hosseini, K.; Mirzazadeh, M.; Baleanu, D.; Raza, N.; Park, C.; Ahmadian, A.; Salahshour, S.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In the present work, the generalized complex Ginzburg-Landau (GCGL) model is considered and its 1-soliton solutions involving different wave structures are retrieved through a series of newly well-organized methods. More exactly, after considering the GCGL model, its 1-soliton solutions are obtained using the exponential and Kudryashov methods in the presence of perturbation effects. As a case study, the effect of various parameter regimes on the dynamics of the dark and bright soliton solutions is analyzed in three- and two-dimensional postures. The validity of all the exact solutions presented in this study has been examined successfully through the use of the symbolic computation system.
Citation - WoS: 23
Citation - Scopus: 23
The Generalized Sasa-Satsuma Equation and Its Optical Solitons
(Springer, 2022) Hosseini, K.; Sadri, K.; Salahshour, S.; Baleanu, D.; Mirzazadeh, M.; Inc, Mustafa; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
The principal goal of the presented paper is to investigate the dynamics of optical solitons for the generalized Sasa-Satsuma (GSS) equation describing the propagation of the femtosecond pulses in the systems of optical fiber transmission. More precisely, the governing model, which is a generalized version of the classical Sasa-Satsuma equation, is firstly reduced in a one-dimensional real regime through a specific transformation; then, its bright and dark optical solitons are established using the modified Kudryashov (MK) method. The changes in the amplitude of the bright and dark solitons are analyzed as a case study for various classes of free parameters. Considerable changes are observed in the optical solitons amplitude from the results presented in the current study.
Citation - WoS: 23
Citation - Scopus: 23
The Geophysical Kdv Equation: Its Solitons, Complexiton, and Conservation Laws
(Springer Heidelberg, 2022) Hosseini, K.; Akbulut, A.; Baleanu, D.; Salahshour, S.; Mirzazadeh, M.; Akinyemi, L.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
The main goal of the current paper is to analyze the impact of the Coriolis parameter on nonlinear waves by studying the geophysical KdV equation. More precisely, specific transformations are first adopted to derive one-dimensional and operator forms of the governing model. Solitons and complexiton of the geophysical KdV equation are then retrieved with the help of several well-established approaches such as the Kudryashov and Hirota methods. In the end, the new conservation theorem given by Ibragimov is formally employed to extract conservation laws of the governing model. It is shown that by increasing the Coriolis parameter, based on the selected parameter regimes, less time is needed for tending the free surface elevation to zero.
Citation - Scopus: 4
Ion-Acoustic Solitons in Magnetized Plasma Under Weak Relativistic Effects on the Electrons
(Springer, 2023) Madhukalya, B.; Das, R.; Hosseini, K.; Baleanu, D.; Salahshour, S.; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
Investigating ion-acoustic disturbances in a magnetized plasma, consisting of relativistic electrons and non-thermal ions, entails a comprehensive study into the nonlinear wave structure. By condensing the fundamental set of fluid equations for the flow variables, a singular equation known as the Sagdeev potential equation is derived using the pseudopotential approach. In this investigation of the magnetized relativistic plasma, we have observed only dip (rarefactive) (N< 1) soliton under both subsonic (M< 1) and supersonic (M> 1) conditions. The occurrence of the soliton depends on the wave velocities in different propagation directions. The magnitude of amplitudes of the relativistic solitons is higher for higher Mach number (M> 1) irrespective of the wave’s propagation direction. Furthermore, the magnitude of amplitudes of the solitary wave is seen to increase near the direction of the magnetic field. © 2023, The Author(s), under exclusive licence to Springer Nature India Private Limited.
Citation - Scopus: 10
The Korteweg-De Vries–caudrey–dodd–gibbon Dynamical Model: Its Conservation Laws, Solitons, and Complexiton
(Shanghai Jiaotong University, 2022) Hosseini, K.; Akbulut, A.; Baleanu, D.; Salahshour, S.; Mirzazadeh, M.; Dehingia, K.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
The main purpose of the present paper is to conduct a detailed and thorough study on the Korteweg-de Vries–Caudrey–Dodd–Gibbon (KdV-CDG) dynamical model. More precisely, after considering the integrable KdV-CDG dynamical model describing certain properties of ocean dynamics, its conservation laws, solitons, and complexiton are respectively derived using the Ibragimov, Kudryashov, and Hirota methods. Several numerical simulations in two and three-dimensional postures are formally given to analyze the effect of nonlinear parameters. It is shown that nonlinear parameters play a key role in the dynamical properties of soliton and complexiton solutions. © 2022
Citation - WoS: 64
Citation - Scopus: 73
M-Fractional Derivative Under Interval Uncertainty: Theory, Properties and Applications
(Pergamon-elsevier Science Ltd, 2018) Ahmadian, A.; Abbasbandy, S.; Baleanu, D.; Salahshour, S.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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 - Scopus: 12
Multi-Complexiton and Positive Multi-Complexiton Structures To a Generalized B-Type Kadomtsev−petviashvili Equation
(Shanghai Jiaotong University, 2022) Hosseini, K.; Baleanu, D.; Rezapour, S.; Salahshour, S.; Mirzazadeh, M.; Samavat, M.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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. © 2022
Citation - Scopus: 10
A New (4 + 1)-Dimensional Burgers Equation: Its Bäcklund Transformation and Real and Complex N -Kink Solitons
(Springer, 2022) Samavat, M.; Mirzazadeh, M.; Salahshour, S.; Baleanu, D.; Hosseini, K.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
Studying the dynamics of solitons in nonlinear evolution equations (NLEEs) has gained considerable interest in the last decades. Accordingly, the search for soliton solutions of NLEEs 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 dispersive waves in nonlinear sciences. Based on the truncated Painlevé expansion, the Bäcklund transformation of the n4D-BE is firstly extracted, then, its real and complex N-kink solitons are derived using the simplified Hirota method. Furthermore, several ansatz methods are formally adopted to obtain a group of other single-kink soliton solutions of the n4D-BE. © 2022, The Author(s), under exclusive licence to Springer Nature India Private Limited.
Citation - WoS: 17
Citation - Scopus: 17
A New Generalized Kdv Equation: Its Lump-Type, Complexiton and Soliton Solutions
(World Scientific Publ Co Pte Ltd, 2022) Hosseini, K.; Salahshour, S.; Baleanu, D.; Mirzazadeh, M.; Dehingia, K.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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 Backlund 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 - WoS: 39
Citation - Scopus: 42
Non-Singular Multi-Complexiton Wave To a Generalized Kdv Equation
(Springer, 2023) Hosseini, K.; Hincal, E.; Baleanu, D.; Obi, O. A.; Salahshour, S.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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 - WoS: 39
Citation - Scopus: 48
A Novel Algorithm Based on the Legendre Wavelets Spectral Technique for Solving the Lane-Emden Equations
(Elsevier, 2020) Salahshour, S.; Ahmadian, A.; Baleanu, D.; Dizicheh, A. Karimi; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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. (C) 2020 Published by Elsevier B.V. on behalf of IMACS.
Citation - WoS: 33
Citation - Scopus: 41
A Novel Approach To Approximate Fractional Derivative With Uncertain Conditions
(Pergamon-elsevier Science Ltd, 2017) Salahshour, S.; Ali-Akbari, M.; Ismail, F.; Baleanu, D.; Ahmadian, A.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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. (C) 2017 Published by Elsevier Ltd.