Matematik Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413
Browse
3 results
Search Results
Article Citation - WoS: 7Citation - Scopus: 15Hybrid Bernstein Block-Pulse Functions Method for Second Kind Integral Equations With Convergence Analysis(Hindawi Ltd, 2014) Baleanu, Dumitru; Babaei, Fereshteh; Alipour, MohsenWe introduce a new combination of Bernstein polynomials (BPs) and Block-Pulse functions (BPFs) on the interval [0, 1]. These functions are suitable for finding an approximate solution of the second kind integral equation. We call this method Hybrid Bernstein Block-Pulse Functions Method (HBBPFM). This method is very simple such that an integral equation is reduced to a system of linear equations. On the other hand, convergence analysis for this method is discussed. The method is computationally very simple and attractive so that numerical examples illustrate the efficiency and accuracy of this method.Article Citation - WoS: 13Citation - Scopus: 17Approximate Analytical Solution for Nonlinear System of Fractional Differential Equations by Bps Operational Matrices(Hindawi Ltd, 2013) Baleanu, Dumitru; Alipour, MohsenWe present two methods for solving a nonlinear system of fractional differential equations within Caputo derivative. Firstly, we derive operational matrices for Caputo fractional derivative and for Riemann-Liouville fractional integral by using the Bernstein polynomials (BPs). In the first method, we use the operational matrix of Caputo fractional derivative (OMCFD), and in the second one, we apply the operational matrix of Riemann-Liouville fractional integral (OMRLFI). The obtained results are in good agreement with each other as well as with the analytical solutions. We show that the solutions approach to classical solutions as the order of the fractional derivatives approaches 1.Article Citation - WoS: 14Citation - Scopus: 20The Bernstein Operational Matrices for Solving the Fractional Quadratic Riccati Differential Equations With the Riemann-Liouville Derivative(Hindawi Ltd, 2013) Alipour, Mohsen; Jafari, Hossein; Baleanu, DumitruWe obtain the approximate analytical solution for the fractional quadratic Riccati differential equation with the Riemann-Liouville derivative by using the Bernstein polynomials (BPs) operational matrices. In this method, we use the operational matrix for fractional integration in the Riemann-Liouville sense. Then by using this matrix and operational matrix of product, we reduce the problem to a system of algebraic equations that can be solved easily. The efficiency and accuracy of the proposed method are illustrated by several examples.