WoS İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653
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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: 4Citation - Scopus: 4Double-Quasi Numerical Method for the Variable-Order Time Fractional and Riesz Space Fractional Reaction-Diffusion Equation Involving Derivatives in Caputo-Fabrizio Sense(World Scientific Publ Co Pte Ltd, 2020) Pandey, Prashant; Gomez-Aguilar, J. F.; Baleanu, D.; Kumar, SachinOur motive in this scientific contribution is to deal with nonlinear reaction-diffusion equation having both space and time variable order. The fractional derivatives which are used are non-singular having exponential kernel. These derivatives are also known as Caputo-Fabrizio derivatives. In our model, time fractional derivative is Caputo type while spatial derivative is variable-order Riesz fractional type. To approximate the variable-order time fractional derivative, we used a difference scheme based upon the Taylor series formula. While approximating the variable order spatial derivatives, we apply the quasi-wavelet-based numerical method. Here, double-quasi-wavelet numerical method is used to investigate this type of model. The discretization of boundary conditions with the help of quasi-wavelet is discussed. We have depicted the efficiency and accuracy of this method by solving the some particular cases of our model. The error tables and graphs clearly show that our method has desired accuracy.Article Citation - WoS: 66Citation - Scopus: 77Numerical Approach of Fokker-Planck Equation With Caputo-Fabrizio Fractional Derivative Using Ritz Approximation(Elsevier, 2018) Jafari, H.; Lia, A.; Baleanu, D.; Firoozjaee, M. A.In this manuscript, a type of Fokker-Planck equation (FPE) with Caputo-Fabrizio fractional derivative is considered. We present a numerical approach which is based on the Ritz method with known basis functions to transform this equation into an optimization problem. It leads to a nonlinear algebraic system. Then, we obtain the coefficients of basis functions by solving the algebraic system. The convergence of this technique is discussed extensively. Three examples are included to show the applicability and validity of this method. (C) 2017 Elsevier B.V. All rights reserved.Article Citation - WoS: 48Citation - Scopus: 57Solving Fdes With Caputo-Fabrizio Derivative by Operational Matrix Based on Genocchi Polynomials(Wiley, 2018) Roshan, Sedighe Sadeghi; Jafari, Hossein; Baleanu, Dumitru; Sadeghi Roshan, SedigheWe introduce a new approach to solve a type of fractional order differential equations without singularity. For fractional integration, we obtain the operational matrix through Genocchi polynomials. Some examples are presented to test the applicability and efficiency of the technique.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: 47Citation - Scopus: 57Nonlocal Cauchy Problem Via a Fractional Operator Involving Power Kernel in Banach Spaces(Mdpi, 2019) Yavuz, Mehmet; Baleanu, Dumitru; Keten, AysegulWe investigated existence and uniqueness conditions of solutions of a nonlinear differential equation containing the Caputo-Fabrizio operator in Banach spaces. The mentioned derivative has been proposed by using the exponential decay law and hence it removed the computational complexities arising from the singular kernel functions inherit in the conventional fractional derivatives. The method used in this study is based on the Banach contraction mapping principle. Moreover, we gave a numerical example which shows the applicability of the obtained results.