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Ordokhani, Yadollah, Rahimkhani, Parisa, Babolian, Esmail. (1396). Application of fractional-order Bernoulli functions for solving fractional Riccati differential equation. نشریه هنرهای کاربردی, 8(2), 277-292. doi: 10.22075/ijnaa.2017.1476.1379
Yadollah Ordokhani; Parisa Rahimkhani; Esmail Babolian. "Application of fractional-order Bernoulli functions for solving fractional Riccati differential equation". نشریه هنرهای کاربردی, 8, 2, 1396, 277-292. doi: 10.22075/ijnaa.2017.1476.1379
Ordokhani, Yadollah, Rahimkhani, Parisa, Babolian, Esmail. (1396). 'Application of fractional-order Bernoulli functions for solving fractional Riccati differential equation', نشریه هنرهای کاربردی, 8(2), pp. 277-292. doi: 10.22075/ijnaa.2017.1476.1379
Ordokhani, Yadollah, Rahimkhani, Parisa, Babolian, Esmail. Application of fractional-order Bernoulli functions for solving fractional Riccati differential equation. نشریه هنرهای کاربردی, 1396; 8(2): 277-292. doi: 10.22075/ijnaa.2017.1476.1379

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، اسفند 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
تاریخ دریافت: 09 تیر 1395،  تاریخ بازنگری: 12 شهریور 1396،  تاریخ پذیرش: 04 مهر 1396 
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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