Application of fractional-order Bernoulli functions for solving fractional Riccati differential equation | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 24، دوره 8، شماره 2، 2017، صفحه 277-292 اصل مقاله (914.15 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2017.1476.1379 | ||
| نویسندگان | ||
| Yadollah Ordokhani* 1؛ Parisa Rahimkhani2؛ Esmail Babolian3 | ||
| 1Department of Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, Iran | ||
| 2Department of Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, Iran National Elites Foundation, Tehran, Iran | ||
| 3Department of Computer Science, Faculty of Mathematical Sciences and Computer, Kharazmi University, Tehran, Iran | ||
| چکیده | ||
| In 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. | ||
| کلیدواژهها | ||
| Fractional Riccati differential equation؛ Fractional-order Bernoulli functions؛ Caputo derivative؛ Operational matrix؛ Collocation method | ||
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