Matematik Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413
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Article Citation - WoS: 9Citation - Scopus: 11Study on Application of Hybrid Functions To Fractional Differential Equations(Springer international Publishing Ag, 2018) Baleanu, D.; Torkzadeh, L.; Nouri, K.In this study we propose an efficient technique for approximate solution of linear and nonlinear differential equations with fractional order. The operational matrices based upon block-pulse functions and Chebyshev polynomials of the second kind are used for this purpose. Also, we focus on the upper bound of error for performance of the our estimates. The numerical results confirm the convergence of the suggested method. Correspondingly, the obtained results of our method are compared with other approaches in terms of efficiency and accuracy.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.Correction Citation - WoS: 2Citation - Scopus: 1The (K, S)-Fractional Calculus of K-Mittag Function (Vol 2017, 118, 2017)(Springer international Publishing Ag, 2017) Rahman, G.; Baleanu, D.; Mubeen, S.; Arshad, M.; Nisar, K. S.In this note we present some corrections to our previous paperArticle Citation - WoS: 6Citation - Scopus: 9A Method for Solving Nonlinear Volterra's Population Growth Model of Noninteger Order(Springer international Publishing Ag, 2017) Agheli, B.; Firozja, M. Adabitabar; Al Qurashi, M. Mohamed; Baleanu, D.; Adabitabar Firozja, M.Many numerical methods have been developed for nonlinear fractional integro-differential Volterra's population model (FVPG). In these methods, to approximate a function on a particular interval, only a restricted number of points have been employed. In this research, we show that it is possible to use the fuzzy transform method (F-transform) to tackle with FVPG. It makes the F-transform preferable to other methods since it can make full use of all points on this interval. We also make a comparison showing that this method is less computational and is more convenient to be utilized for coping with nonlinear integro-differential equation (IDEs), fractional nonlinear integro-differential equation (FIDEs), and fractional ordinary differential equations (FODEs).