WoS İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653
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Article Citation - WoS: 46Citation - Scopus: 48Solutions of the Fractional Davey-Stewartson Equations With Variational Iteration Method(Editura Acad Romane, 2012) Baleanu, Dumitru; Jafari, Hossain; Kadem, Abdelouahab; Yılmaz, Tuğba; Baleanu, Dumitru; Yilmaz, Tugba; Matematik; PsikolojiThis paper presents approximate analytical solutions for the fractional Davey-Stewartson equations using the Variational iteration method. The fractional derivatives are described in the Caputo sense. This method is based on the incorporation of the correction functional for the equation. The results obtained by this method have been compared with the exact solutions and show that the introduced approach is a promising tool for solving many linear and nonlinear fractional differential equations.Article Citation - WoS: 11Numerical and Bifurcations Analysis for Multi Order Fractional Model of Hiv Infection of Cd4+t-cells(Univ Politehnica Bucharest, Sci Bull, 2016) Alipour, Mohsen; Baleanu, Dumitru; Arshad, Sadia; Baleanu, Dumitru; MatematikIn this paper, we solve the dynamical system of HIV infection of CD4(+) T cells within the multi-order fractional derivatives. The Bernstein operational matrices in arbitrary interval [a,b] are applied to obtain the approximate analytical solution of the model. In this way, the fractional differential equations are reduced to an algebraic easily solvable system. The obtained solutions are accurate and the method is very efficient and simple in implementation. With the help of bifurcation analysis, we acquired the critical value of viral death rate, that is, if viral death rate is greater than the critical value then level of virus particles starts to decline and thus free virus will eventually eliminate and patient is cured. Further, we found the threshold for viral infection rate analytically, which assures the stability of uninfected equilibrium and virus will ultimately eradicate.Article Citation - WoS: 41Citation - Scopus: 41Homotopy Perturbation Method for Solving a System of Schrodinger-Korteweg Vries Equations(Editura Acad Romane, 2011) Golmankhaneh, Alireza K.; Baleanu, Dumitru; Golmankhaneh, Ali K.; Baleanu, Dumitru; MatematikNumerical methods used to find exact solution for the nonlinear differential equations. During the past decades Iterative methods has attracted attention of researcher for solving fractional differential equations. In the present paper, the homotopy perturbation method has been successively used to obtain approximate analytical solutions of the fractional coupled Schrodinger-Korteweg-de Vries and coupled system of diffusion-reaction equation equations. We consider fractional derivative in the Caputo sense. We have illustrated by examples the ability of proposed algorithm for solving fractional system of nonlinear equation.Article Citation - WoS: 52Citation - Scopus: 54Fractional Caputo Heat Equation Within the Double Laplace Transform(Editura Acad Romane, 2013) Jarad, Fahd; Anwar, A. M. O.; Jarad, Fahd; Baleanu, Dumitru; Baleanu, D.; Ayaz, F.; MatematikThe heat equation and its fractional generalization are used in various applications in science and engineering. In this paper firstly we introduce the double Laplace transform of the partial fractional integrals and derivatives which can be used to solve partial differential equations with Caputo fractional derivatives. Secondly, the fractional heat equation was investigated in details with the help of this new generalized transformArticle Citation - WoS: 6Citation - Scopus: 8The Role of Obesity in Fractional Order Tumor-Immune Model(Univ Politehnica Bucharest, Sci Bull, 2020) Arshad, Sadia; Baleanu, Dumitru; Yildiz, Tugba Akman; Baleanu, Dumitru; Tang, Yifa; MatematikThis work investigates the tumor-obesity model via a fractional operator to analyze the interactions between cancer and obesity, since fractional derivatives capture the long formation of cancerous tumor cells that might takes years to develop. It is known that fat cells enhance the development of cancerous tumor cells. To examine how the immune system is influenced due to fat cells, interactions of four types of cell population, namely tumor cells, immune cells, normal cells and fat cells are examined. We investigate the equilibrium points and discuss their stability analytically. Numerical simulations are carried out to verify the analytical results, demonstrating that a low fat diet results in a smaller tumor burden as compared to a high-caloric diet.Article Citation - WoS: 11Citation - Scopus: 14Numerical and Bifurcations Analysis for Multi Order Fractional Model of Hiv Infection of Cd4<sup>+</Sup>t-cells(Univ Politehnica Bucharest, Sci Bull, 2016) Alipour, Mohsen; Arshad, Sadia; Baleanu, DumitruIn this paper, we solve the dynamical system of HIV infection of CD4(+) T cells within the multi-order fractional derivatives. The Bernstein operational matrices in arbitrary interval [a,b] are applied to obtain the approximate analytical solution of the model. In this way, the fractional differential equations are reduced to an algebraic easily solvable system. The obtained solutions are accurate and the method is very efficient and simple in implementation. With the help of bifurcation analysis, we acquired the critical value of viral death rate, that is, if viral death rate is greater than the critical value then level of virus particles starts to decline and thus free virus will eventually eliminate and patient is cured. Further, we found the threshold for viral infection rate analytically, which assures the stability of uninfected equilibrium and virus will ultimately eradicate.Article Citation - WoS: 9Citation - Scopus: 9A High-Accuracy Vieta-Fibonacci Collocation Scheme To Solve Linear Time-Fractional Telegraph Equations(Taylor & Francis Ltd, 2022) Sadri, Khadijeh; Hosseini, Kamyar; Baleanu, Dumitru; Salahshour, SoheilThe 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.Article Citation - WoS: 22Citation - Scopus: 28Non-Instantaneous Impulsive Fractional Integro-Differential Equations With State-Dependent Delay Br(Univ Maragheh, 2022) Salim, Abdelkrim; Aissani, Khalida; Benchohra, Mouffak; Karapinar, Erdal; Benkhettou, NadiaThis paper deals with the existence and uniqueness of the mild solution of the fractional integro-differential equations with non-instantaneous impulses and state-dependent delay. Our arguments are based on the fixed point theory. Finally, an example to confirm of the results is provided.Article Citation - WoS: 4Citation - Scopus: 5Spectral Solutions for a Class of Nonlinear Wave Equations With Riesz Fractional Based on Legendre Collocation Technique(Elsevier, 2023) Abdelkawy, M. A.; Soluma, E. M.; Al-Dayel, Ibrahim; Baleanu, DumitruA numerical investigation is presented in this work for a class of Riesz space-fractional nonlinear wave equations (MD-RSFN-WEs). The presence of a spatial Laplacian of fractional order, stated by fractional Riesz derivatives, is taken into consideration by the model. The fractional wave equation governs mechanical diffusive wave propagation in viscoelastic medium with power-law creep and, as a result, gives a physical under-standing of this equation within the context of dynamic viscoelasticity. To deal with the independent variables, a totally spectral collocation approach is used. Our approach has shown to be more precise, efficient, and practical for the present model. The findings demonstrated that the spectral scheme is exponentially convergent.(c) 2022 Elsevier B.V. All rights reserved.Article Citation - WoS: 36Citation - Scopus: 36All Linear Fractional Derivatives With Power Functions' Convolution Kernel and Interpolation Properties(Pergamon-elsevier Science Ltd, 2023) Baleanu, Dumitru; Shiri, BabakOur attempt is an axiomatic approach to find all classes of possible definitions for fractional derivatives with three axioms. In this paper, we consider a special case of linear integro-differential operators with power functions' convolution kernel a(a)(t-s)b(a) of order a a (0,1). We determine analytic functions a(a) and b(a) such that when a-* 0+, the corresponding operator becomes identity operator, and when a-* 1- the corresponding operator becomes derivative operator. Then, a sequential operator is used to extend the fractional operator to a higher order. Some properties of the sequential operator in this regard also are studied. The singularity properties, Laplace transform and inverse of the new class of fractional derivatives are investigated. Several examples are provided to confirm theoretical achievements. Finally, the solution of the relaxation equation with diverse fractional derivatives is obtained and compared.
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