Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-68228220171201Application of fractional-order Bernoulli functions for solving fractional Riccati differential equation277292279510.22075/ijnaa.2017.1476.1379ENYadollah OrdokhaniDepartment of Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, IranParisa RahimkhaniDepartment of Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, Iran
National Elites Foundation, Tehran, IranEsmail BabolianDepartment of Computer Science, Faculty of Mathematical Sciences and Computer, Kharazmi University, Tehran, IranJournal Article20160629In this paper, a new numerical method for solving the fractional Riccati differential equation is presented. The fractional derivatives are described in the Caputo sense. The method is based upon fractional-order Bernoulli functions approximations. First, the fractional-order Bernoulli functions and their properties are presented. Then, an operational matrix of fractional order integration is derived and is utilized to reduce the under study problem to a system of algebraic equations. Error analysis included the residual error estimation and the upper bound of the absolute errors are introduced for this method. The technique and the error analysis are applied to some problems to demonstrate the validity and applicability of our method.http://ijnaa.semnan.ac.ir/article_2795_3990006fa9915eb0af3345e8046f7bc8.pdf