Matematik Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413
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Article Citation - WoS: 15Citation - Scopus: 17Robust Synchronization of Multi-Weighted Fractional Order Complex Dynamical Networks Under Nonlinear Coupling Via Non-Fragile Control With Leakage and Constant Delays(Pergamon-elsevier Science Ltd, 2023) Raja, R.; Dianavinnarasi, J.; Alzabut, J.; Baleanu, D.; Aadhithiyan, S.In this article, we examine the impact of leakage delays on robust synchronization for fractional order multi-weighted complex dynamical networks(MFCDN) under non-linear coupling via non-fragile control. By employing the fractional order comparison principle, suitable Lyapunov method, and some fractional order inequality techniques, we ensured the robust asymptotical synchronization for MFCDN. In addition to common findings, we have done some specific research in order to get reliable synchronization for multi-weighted complex dynamical network(MCDN) without leakage delay. Additionally, our findings gained are applicable to single weighted FCDN and integer order complex dynamical networks, regardless of whether they have a single weight or many weights. Our suggested approach is shown to be more effective and practical in this article by providing a numerical simulation.Article Citation - WoS: 101Citation - Scopus: 116An Efficient Computational Approach for a Fractional-Order Biological Population Model With Carrying Capacity(Pergamon-elsevier Science Ltd, 2020) Dubey, V. P.; Kumar, R.; Singh, J.; Kumar, D.; Baleanu, D.; Srivastava, H. M.In this article, we examine a fractional-order biological population model with carrying capacity. The blended homotopy techniques pertaining to the Sumudu transform are utilized to explore the solutions of a nonlinear fractional-order population model with carrying capacity. The fractional derivative of the Caputo type is utilized in the proposed investigation. The numerical computations indicate the sufficiency of the iterations for the improved estimations of the solutions of this fractional-order biological population model which exemplifies the potency and soundness of the utilized schemes. The analysis explored through the utilization of the projected methods reveals that both of the schemes are in a great agreement with each other. The variations of the prey and predator populations with respect to time and fractional order of the Caputo derivative are presented and graphically illustrated. (c) 2020 Elsevier Ltd. All rights reserved.Article Citation - WoS: 32Citation - Scopus: 40Comparative Study for Optimal Control Nonlinear Variable -Order Fractional Tumor Model(Pergamon-elsevier Science Ltd, 2020) AL-Mekhlafi, S. M.; Alshomrani, A. S.; Baleanu, D.; Sweilam, N. H.Article Citation - WoS: 82Citation - Scopus: 86Controllability of Semilinear Impulsive Atangana-Baleanu Fractional Differential Equations With Delay(Pergamon-elsevier Science Ltd, 2019) Baleanu, D.; Seba, D.; Aimene, D.We discuss the controllability of semilinear differential equations of fractional order with impulses and delay. We make use of the Atangana-Baleanu derivative. Our main tools are semigroup theory, the fixed point theorem due to Darbo and their combination with the properties of measures of noncompactness. Our abstract results are well supported by an illustrative example. (C) 2019 Published by Elsevier Ltd.Article Citation - WoS: 5Citation - Scopus: 6Analytic Solution for a Nonlinear Problem of Magneto-Thermoelasticity(Pergamon-elsevier Science Ltd, 2013) Ghaderi, P.; Golmankhaneh, Alireza K.; Baleanu, D.; Jafarian, A.In this paper, we present a comparative study of the homotopy analysis method (HAM), the variational iteration method (VIM) and the iterative method (He's polynomials). The approximate solution of the coupled harmonic waves nonlinear magneto-thermoelasticity equations under influence of rotation is obtained. In order to control and adjust the convergence region and the rate of solution series, we show that it is possible to choose a valid auxiliary parameter h of HAM. Using the boundary and the initial conditions we select a suitable initial approximation. The results show that these methods are very efficient, convenient and applicable to a large class of problems.Article Citation - WoS: 134Citation - Scopus: 160A New Approach for Solving a System of Fractional Partial Differential Equations(Pergamon-elsevier Science Ltd, 2013) Nazari, M.; Baleanu, D.; Khalique, C. M.; Jafari, H.In this paper we propose a new method for solving systems of linear and nonlinear fractional partial differential equations. This method is a combination of the Laplace transform method and the Iterative method and here after called the Iterative Laplace transform method. This method gives solutions without any discretization and restrictive assumptions. The method is free from round-off errors and as a result the numerical computations are reduced. The fractional derivative is described in the Caputo sense. Finally, numerical examples are presented to illustrate the preciseness and effectiveness of the new technique. (C) 2012 Elsevier Ltd. All rights reserved.Article Citation - WoS: 89Citation - Scopus: 93A Spectral Legendre-Gauss Collocation Method for A Space-Fractional Advection Diffusion Equations With Variable Coefficients(Pergamon-elsevier Science Ltd, 2013) Baleanu, D.; Bhrawy, A. H.An efficient Legendre-Gauss-Lobatto collocation (L-GL-C) method is applied to solve the space-fractional advection diffusion equation with nonhomogeneous initial-boundary conditions. The Legendre-Gauss-Lobatto points are used as collocation nodes for spatial fractional derivatives as well as the Caputo fractional derivatiye. This approach is reducing the problem to the solution of a system of ordinary differential equations in time which can be solved by using any standard numerical techniques. The proposed numerical solutions when compared with the exact solutions reveal that the obtained solution produces highly accurate results. The results show that the proposed method has high accuracy and is efficient for solving the space-fractional advection diffusion equation.Article Citation - WoS: 134Citation - Scopus: 154A New Approach for Solving Multi Variable Orders Differential Equations With Mittag-Leffler Kernel(Pergamon-elsevier Science Ltd, 2020) Jafari, H.; Baleanu, D.; Ganji, R. M.In this paper we consider multi variable orders differential equations (MVODEs) with non-local and no-singular kernel. The derivative is described in Atangana and Baleanu sense of variable order. We use the fifth-kind Chebyshev polynomials as basic functions to obtain operational matrices. We transfer the original equations to a system of algebraic equations using operational matrices and collocation method. The convergence analysis of the presented method is discussed. Few examples are presented to show the efficiency of the presented method. (C) 2019 Elsevier Ltd. All rights reserved.Article Citation - WoS: 95Citation - Scopus: 109Collocation Methods for Fractional Differential Equations Involving Non-Singular Kernel(Pergamon-elsevier Science Ltd, 2018) Shiri, B.; Baleanu, D.A system of fractional differential equations involving non-singular Mittag-Leffler kernel is considered. This system is transformed to a type of weakly singular integral equations in which the weak singular kernel is involved with both the unknown and known functions. The regularity and existence of its solution is studied. The collocation methods on discontinuous piecewise polynomial space are considered. The convergence and superconvergence properties of the introduced methods are derived on graded meshes. Numerical results provided to show that our theoretical convergence bounds are often sharp and the introduced methods are efficient. Some comparisons and applications are discussed. (C) 2018 Elsevier Ltd. All rights reserved.Article Citation - WoS: 65Citation - Scopus: 74M-Fractional Derivative Under Interval Uncertainty: Theory, Properties and Applications(Pergamon-elsevier Science Ltd, 2018) Ahmadian, A.; Abbasbandy, S.; Baleanu, D.; Salahshour, S.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.