WoS İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653
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Article Citation - WoS: 12Citation - Scopus: 21Generalized Invexity and Duality in Multiobjective Variational Problems Involving Non-Singular Fractional Derivative(de Gruyter Poland Sp Z O O, 2022) Kumar, Devendra; Alshehri, Hashim M.; Singh, Jagdev; Baleanu, Dumitru; Dubey, Ved PrakashIn this article, we extend the generalized invexity and duality results for multiobjective variational problems with fractional derivative pertaining to an exponential kernel by using the concept of weak minima. Multiobjective variational problems find their applications in economic planning, flight control design, industrial process control, control of space structures, control of production and inventory, advertising investment, impulsive control problems, mechanics, and several other engineering and scientific problems. The proposed work considers the newly derived Caputo-Fabrizio (CF) fractional derivative operator. It is actually a convolution of the exponential function and the first-order derivative. The significant characteristic of this fractional derivative operator is that it provides a non-singular exponential kernel, which describes the dynamics of a system in a better way. Moreover, the proposed work also presents various weak, strong, and converse duality theorems under the diverse generalized invexity conditions in view of the CF fractional derivative operator.Article Citation - WoS: 61Citation - Scopus: 83Impulsive Caputo-Fabrizio Fractional Differential Equations in B-Metric Spaces(de Gruyter Poland Sp Z O O, 2021) Abbas, Said; Benchohra, Mouffak; Karapinar, Erdal; Lazreg, Jamal Eddine; Karaplnar, ErdalWe deal with some impulsive Caputo-Fabrizio fractional differential equations in b-metric spaces. We make use of alpha-phi-Geraghty-type contraction. An illustrative example is the subject of the last section.Article Citation - WoS: 13Citation - Scopus: 14A New Numerical Method for Time Fractional Non-Linear Sharma-Tasso Equation and Klein-Gordon Equation With Exponential Kernel Law(Frontiers Media Sa, 2020) Baleanu, Dumitru; Kumar, SachinIn this work, we derived a novel numerical scheme to find out the numerical solution of fractional PDEs having Caputo-Fabrizio (C-F) fractional derivatives. We first find out the formula of approximation for the C-F derivative of the function f(t) = t(k). We approximate the C-F derivative in time direction with the help of Legendre spectral method and approximation formula of t(k). The unknown function and their derivatives in spatial direction are approximated with the help of the method which is based on a quasi wavelet. We implement this newly derived method to solve the non-linear Sharma-Tasso-Oliver equation and non-linear Klein-Gordon equation in which time-fractional derivative is of C-F type. The accuracy and validity of this new method are depicted by giving the numerical solution of some numerical examples. The numerical results for the particular cases of Klein-Gordon equation are compared with the existing exact solutions and from the obtained error we can conclude that our proposed numerical method achieves accurate results. The effect of time-fractional exponent alpha on the solution profile is characterized by figures. The comparison of solution profile u(x, t) for different type time-fractional derivative (C-F vs. Caputo) is depicted by figures.Article Citation - WoS: 268Citation - Scopus: 281Caputo-Fabrizio Derivative Applied To Groundwater Flow Within Confined Aquifer(Asce-amer Soc Civil Engineers, 2017) Baleanu, Dumitru; Atangana, AbdonThe model of the movement of subsurface water via the geological formation called aquifer was extended using a newly proposed derivative with fractional order. An alternative derivative to that of Caputo-Fabrizio with fractional order was presented. The relationship between both derivatives was presented. The new equation was solved analytically using some integral transforms. The exact solution is therefore compared to experimental data obtained from the settlement of the University of the Free State in South Africa. The numerical simulation shows the agreement of the experimental data with an analytical solution for some values of fractional order. (C) 2016 American Society of Civil Engineers.Article Citation - WoS: 31Citation - Scopus: 33Analysis of a New Fractional Model for Damped Bergers' Equation(de Gruyter Open Ltd, 2017) Kumar, Devendra; Al Qurashi, Maysaa; Baleanu, Dumitru; Singh, JagdevIn this article, we present a fractional model of the damped Bergers' equation associated with the Caputo-Fabrizio fractional derivative. The numerical solution is derived by using the concept of an iterative method. The stability of the applied method is proved by employing the postulate of fixed point. To demonstrate the effectiveness of the used fractional derivative and the iterative method, numerical results are given for distinct values of the order of the fractional derivative.Article Citation - WoS: 51Citation - Scopus: 88Chaos in a Cancer Model Via Fractional Derivatives With Exponential Decay and Mittag-Leffler Law(Mdpi, 2017) Guadalupe Lopez-Lopez, Maria; Manuel Alvarado-Martinez, Victor; Baleanu, Dumitru; Khan, Hasib; Francisco Gomez-Aguilar, Jose; Alvarado-Martínez, Victor Manuel; Gómez-Aguilar, José Francisco; López-López, María GuadalupeIn this paper, a three-dimensional cancer model was considered using the Caputo-Fabrizio-Caputo and the new fractional derivative with Mittag-Leffler kernel in Liouville-Caputo sense. Special solutions using an iterative scheme via Laplace transform, Sumudu-Picard integration method and Adams-Moulton rule were obtained. We studied the uniqueness and existence of the solutions. Novel chaotic attractors with total order less than three are obtained.