Browsing by Author "Ahmadian, A."

Now showing 1 - 13 of 13

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 - 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: 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: 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 - 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.
Citation - WoS: 11
Citation - Scopus: 17
Numerical Study of Third-Order Ordinary Differential Equations Using a New Class of Two Derivative Runge-Kutta Type Methods
(Elsevier, 2020) Senu, N.; Ahmadian, A.; Ibrahim, S. N. I.; Baleanu, D.; Lee, K. C.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
This study introduces new special two-derivative Runge-Kutta type (STDRKT) methods involving the fourth derivative of the solution for solving third-order ordinary differential equa-tions. In this regards, rooted tree theory and the corresponding B-series theory is proposed to derive order conditions for STDRKT methods. Besides, explicit two-stages fifth order and three-stages sixth order STDRKT methods are derived and stability,consistency and convergence of STDRKT methods are analysed in details. Accuracy and effectiveness of the proposed techniques are vali-dated by a number of various test problems and compared to existing methods in the literature. (C) 2020 The Authors. Published by Elsevier B.V. on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).
Citation - WoS: 135
Citation - Scopus: 151
Solving Differential Equations of Fractional Order Using an Optimization Technique Based on Training Artificial Neural Network
(Elsevier Science inc, 2017) Ahmadian, A.; Effati, S.; Salahshour, S.; Baleanu, D.; Pakdaman, M.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
The current study aims to approximate the solution of fractional differential equations (FDEs) by using the fundamental properties of artificial neural networks (ANNs) for function approximation. In the first step, we derive an approximate solution of fractional differential equation (FDE) by using ANNs. In the second step, an optimization approach is exploited to adjust the weights of ANNs such that the approximated solution satisfies the FDE. Different types of FDEs including linear and nonlinear terms are solved to illustrate the ability of the method. In addition, the present scheme is compared with the analytical solution and a number of existing numerical techniques to show the efficiency of ANNs with high accuracy, fast convergence and low use of memory for solving the FDEs. (C) 2016 Elsevier Inc. All rights reserved.
Citation - WoS: 4
Citation - Scopus: 3
Some Kinds of the Controllable Problems for Fuzzy Control Dynamic Systems
(Asme, 2018) Tri, P. V.; Ahmadian, A.; Salahshour, S.; Baleanu, D.; Phu, N. D.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this work, we have discussed the fuzzy solutions for fuzzy controllable problem, fuzzy feedback problem, and fuzzy global controllable (GC) problems. We use the method of successive approximations under the generalized Lipschitz condition for the local existence and furthermore, we have described the contraction principle under suitable conditions for global existence and uniqueness of fuzzy solutions. We have too the GC results for fuzzy systems. Some examples and computer simulation illustrating our approach are also given for these controllable problems.
Citation - WoS: 61
Citation - Scopus: 69
Tau Method for the Numerical Solution of a Fuzzy Fractional Kinetic Model and Its Application To the Oil Palm Frond as a Promising Source of Xylose
(Academic Press inc Elsevier Science, 2015) Salahshour, S.; Baleanu, D.; Amirkhani, H.; Yunus, R.; Ahmadian, A.; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
The Oil Palm Frond (a lignocellulosic material) is a high-yielding energy crop that can be utilized as a promising source of xylose. It holds the potential as a feedstock for bioethanol production due to being free and inexpensive in terms of collection, storage and cropping practices. The aim of the paper is to calculate the concentration and yield of xylose from the acid hydrolysis of the Oil Palm Frond through a fuzzy fractional kinetic model. The approximate solution of the derived fuzzy fractional model is achieved by using a tau method based on the fuzzy operational matrix of the generalized Laguerre polynomials. The results validate the effectiveness and applicability of the proposed solution method for solving this type of fuzzy kinetic model. (C) 2015 Elsevier Inc. All rights reserved.
Citation - WoS: 90
Citation - Scopus: 101
Uncertain Viscoelastic Models With Fractional Order: a New Spectral Tau Method To Study the Numerical Simulations of the Solution
(Elsevier Science Bv, 2017) Ismail, F.; Salahshour, S.; Baleanu, D.; Ghaemi, F.; Ahmadian, A.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
The analysis of the behaviors of physical phenomena is important to discover significant features of the character and the structure of mathematical models. Frequently the unknown parameters involve in the models are assumed to be unvarying over time. In reality, some of them are uncertain and implicitly depend on several factors. In this study, to consider such uncertainty in variables of the models, they are characterized based on the fuzzy notion. We propose here a new model based on fractional calculus to deal with the Kelvin-Voigt (KV) equation and non-Newtonian fluid behavior model with fuzzy parameters. A new and accurate numerical algorithm using a spectral tau technique based on the generalized fractional Legendre polynomials (GFLPs) is developed to solve those problems under uncertainty. Numerical simulations are carried out and the analysis of the results highlights the significant features of the new technique in comparison with the previous findings. A detailed error analysis is also carried out and discussed. (C) 2017 Elsevier B.V. All rights reserved.
Citation - WoS: 8
Citation - Scopus: 10
Variation of Constant Formula for the Solution of Interval Differential Equations of Non-Integer Order
(Springer Heidelberg, 2017) Ahmadian, A.; 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 inherits the classical properties from the first order derivative. Therefore, we propose in this research a new strategy to acquire interval solution of fractional interval differential equations (FIDEs) under interval fractional conformable derivative. This scheme is developed based on a variation of the constant formula to achieve the solution explicitly. The important characteristic of this technique is that it helps us to find a solution with decreasing length of its support which is critical for the solutions based on the interval or fuzzy notions. Two examples are experienced to illustrate our approach and validate it.