WoS İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653
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Article Citation - WoS: 25Citation - Scopus: 27Solution of Modified Bergman Minimal Blood Glucose-Insulin Model Using Caputo-Fabrizio Fractional Derivative(Tech Science Press, 2021) Baleanu, Dumitru; Mishra, Manvendra Narayan; Goswami, Pranay; Dubey, Ravi ShankerDiabetes is a burning issue in the whole world. It is the imbalance between body glucose and insulin. The study of this imbalance is very much needed from a research point of view. For this reason, Bergman gave an important model named-Bergman minimal model. In the present work, using Caputo-Fabrizio (CF) fractional derivative, we generalize Bergman's minimal blood glucose-insulin model. Further, we modify the old model by including one more component known as diet D(t), which is also essential for the blood glucose model. We solve the modified model with the help of Sumudu transform and fixed-point iteration procedures. Also, using the fixed point theorem, we examine the existence and uniqueness of the results along with their numerical and graphical representation. Furthermore, the comparison between the values of parameters obtained by calculating different values of t with experimental data is also studied. Finally, we draw the graphs of G(t), X(t), I(t), and D(t) for different values of tau. It is also clear from the obtained results and their graphical representation that the obtained results of modified Bergman's minimal model are better than Bergman's model.Article Citation - WoS: 6Citation - Scopus: 8Recovering the Space Source Term for the Fractional-Diffusion Equation With Caputo-Fabrizio Derivative(Springer, 2021) Nguyen Hoang Luc; Baleanu, Dumitru; Le Dinh Long; Le Nhat Huynh; Long, Le Dinh; Huynh, Le Nhat; Luc, Nguyen HoangThis article is devoted to the study of the source function for the Caputo-Fabrizio time fractional diffusion equation. This new definition of the fractional derivative has no singularity. In other words, the new derivative has a smooth kernel. Here, we investigate the existence of the source term. Through an example, we show that this problem is ill-posed (in the sense of Hadamard), and the fractional Landweber method and the modified quasi-boundary value method are used to deal with this inverse problem and the regularized solution is also obtained. The convergence estimates are addressed for the regularized solution to the exact solution by using an a priori regularization parameter choice rule and an a posteriori parameter choice rule. In addition, we give a numerical example to illustrate the proposed method.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: 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.Article Citation - WoS: 9Citation - Scopus: 10Hardy-Type Inequalities Within Fractional Derivatives Without Singular Kernel(Springeropen, 2018) Baleanu, Dumitru; Basci, YaseminIn this manuscript, we developed the Hardy-type inequality within the Caputo-Fabrizio fractional derivative. We presented some illustrative examples to confirm our work.Article Citation - WoS: 9Citation - Scopus: 11New Aspects of Opial-Type Integral Inequalities(Springeropen, 2018) Baleanu, Dumitru; Basci, YaseminIn this manuscript, we prove new aspects for several Opial-type integral inequalities for the left and right Caputo-Fabrizio operators with nonsingular kernel. For this purpose we use the inequalities obtained by Andri et al. (Integral Transforms Spec. Funct. 25(4):324-335, 2014), which is the generalization of an inequality of Agarwal and Pang (Opial Inequalities with Applications in Differential and Difference Equations, 1995). Besides, examples are presented to validate the reported results.