Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
Browse
20 results
Search Results
Article Citation - WoS: 7Citation - Scopus: 10Common Fixed Point Theorems for Generalized (φ,ψ)-Weak Contraction Condition in Complete Metric Spaces(Springer international Publishing Ag, 2015) Tas, Kenan; Patel, Uma Devi; Murthy, Penumarthy ParvateesamThe intent of this manuscript is to establish some common fixed point theorems in a complete metric space under weak contraction condition for two pairs of discontinuous weak compatible maps. The results proved herein are the generalization of some recent results in literature. We give an example to support our results.Article Citation - WoS: 25Citation - Scopus: 29A New Approach for One-Dimensional Sine-Gordon Equation(Springer international Publishing Ag, 2016) Inc, Mustafa; Kilicman, Adem; Baleanu, Dumitru; Akgul, AliIn this work, we use a reproducing kernel method for investigating the sine-Gordon equation with initial and boundary conditions. Numerical experiments are studied to show the efficiency of the technique. The acquired results are compared with the exact solutions and results obtained by different methods. These results indicate that the reproducing kernel method is very effective.Article Citation - WoS: 23Citation - Scopus: 26Numerical Solution of Linear Integral Equations System Using the Bernstein Collocation Method(Springer international Publishing Ag, 2013) Nia, Safa A. Measoomy; Golmankhaneh, Alireza K.; Baleanu, Dumitru; Jafarian, AhmadSince in some application mathematical problems finding the analytical solution is too complicated, in recent years a lot of attention has been devoted by researchers to find the numerical solution of this equations. In this paper, an application of the Bernstein polynomials expansion method is applied to solve linear second kind Fredholm and Volterra integral equations systems. This work reduces the integral equations system to a linear system in generalized case such that the solution of the resulting system yields the unknown Bernstein coefficients of the solutions. Illustrative examples are provided to demonstrate the preciseness and effectiveness of the proposed technique. The results are compared with the exact solution by using computer simulations.Article Citation - WoS: 52Citation - Scopus: 57On a Nonlinear Fractional Differential Equation on Partially Ordered Metric Spaces(Springer international Publishing Ag, 2013) Mohammadi, Hakimeh; Rezapour, Shahram; Baleanu, DumitruIn this paper, by using a fixed point result on ordered metric spaces, we prove the existence and uniqueness of a solution of the nonlinear fractional differential equation (, ) via the periodic boundary condition , where and is a continuous increasing function and denotes the Caputo fractional derivative of order alpha. Also, we solve it by using the anti-periodic boundary conditions with and with and separately.Article Citation - WoS: 96Citation - Scopus: 117A Jacobi Operational Matrix for Solving a Fuzzy Linear Fractional Differential Equation(Springer international Publishing Ag, 2013) Suleiman, Mohamed; Salahshour, Soheil; Baleanu, Dumitru; Ahmadian, AliThis paper reveals a computational method based using a tau method with Jacobi polynomials for the solution of fuzzy linear fractional differential equations of order . A suitable representation of the fuzzy solution via Jacobi polynomials diminishes its numerical results to the solution of a system of algebraic equations. The main advantage of this method is its high robustness and accuracy gained by a small number of Jacobi functions. The efficiency and applicability of the proposed method are proved by several test examples.Article Citation - WoS: 23Citation - Scopus: 49Existence Results for Fractional Neutral Functional Integro-Differential Evolution Equations With Infinite Delay in Banach Spaces(Springer international Publishing Ag, 2013) Baleanu, Dumitru; Ravichandran, ChokkalingamIn this paper, we investigate the existence results for a class of abstract fractional neutral integro-differential evolution systems involving the Caputo derivative in Banach spaces. The main techniques rely on the fractional calculus, properties of characteristic solution operators, Monch's fixed point theorem via measures of noncompactness. Particularly, we do not assume that characteristic solution operators are compact. The application is given to illustrate the theory. The results of this article are generalization and improvement of the recent results on this issue. MSC: 26A33, 34A12, 47H08, 47H10.Article Citation - WoS: 84Citation - Scopus: 98Hiv/Hcv Coinfection Model: a Fractional-Order Perspective for the Effect of the Hiv Viral Load(Springer international Publishing Ag, 2018) Pinto, Carla M. A.; Baleanu, Dumitru; Carvalho, Ana R. M.We study the burden of the HIV viremia and of treatment efficacy in the severity of the patterns of the HIV/HCV coinfection. For this, we derive a simple non-integer-order (fractional-order) model for the coinfection dynamics. Fractional-order models have been proved in the literature to provide good fits to real data from patients suffering from several diseases, such as HIV, dengue fever, and others. We have computed the basic reproduction number and the stability of the disease-free equilibrium of the model. The numerical results suggest that the HIV viral load impacts impressively the severity of the HCV infection. The treatment efficacy is also found to influence the natural progression of HCV on the HIV/HCV coinfection. The latter is repeated for all values of the order of the fractional derivative. Moreover, the fractional derivative may pave the way to better understanding the individuals' patients' adjustments to treatment and to viremia.Article Citation - WoS: 20Citation - Scopus: 28Operational Matrix Approach for Solving the Variable-Order Nonlinear Galilei Invariant Advection-Diffusion Equation(Springer international Publishing Ag, 2018) Baleanu, D.; Alzaidy, J. F.; Hashemizadeh, E.; Zaky, M. A.In this paper, we investigate numerical solution of the variable-order fractional Galilei advection-diffusion equation with a nonlinear source term. The suggested method is based on the shifted Legendre collocation procedure and a matrix form representation of variable-order Caputo fractional derivative. The main advantage of the proposed method is investigating a global approximation for the spatial and temporal discretizations. This method reduces the problem to a system of algebraic equations, which is easier to solve. The validity and effectiveness of the method are illustrated by an easy-to-follow example.Article Citation - WoS: 61Citation - Scopus: 64On the Existence of Solutions of a Three Steps Crisis Integro-Differential Equation(Springer international Publishing Ag, 2018) Ghafarnezhad, Khadijeh; Rezapour, Shahram; Shabibi, Mehdi; Baleanu, DumitruThere are many natural phenomena including a crisis (such as a spate or contest) which could be described in three steps. We investigate the existence of solutions for a three step crisis integro-differential equation. We suppose that the second step is a point-wise defined singular fractional differential equation.Article Citation - WoS: 45Citation - Scopus: 71On Solutions of Fractional Riccati Differential Equations(Springer international Publishing Ag, 2017) Akgul, Ali; Baleanu, Dumitru; Sakar, Mehmet GiyasWe apply an iterative reproducing kernel Hilbert space method to get the solutions of fractional Riccati differential equations. The analysis implemented in this work forms a crucial step in the process of development of fractional calculus. The fractional derivative is described in the Caputo sense. Outcomes are demonstrated graphically and in tabulated forms to see the power of the method. Numerical experiments are illustrated to prove the ability of the method. Numerical results are compared with some existing methods.