Application of fractional-order Bernoulli functions for solving fractional Riccati di erential equation

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Rahimkhani Parisa; ORDOKHANI YADOLLAH; Babolian Esmail

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Journal Paper

Paper Information

Journal: INTERNATIONAL JOURNAL OF NONLINEAR ANALYSIS AND APPLICATIONS Year:2017 | Volume:8 | Issue:2 Page(s): 277-292

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Information Journal Paper

Title

Application of fractional-order Bernoulli functions for solving fractional Riccati di erential equation

Author(s)

Rahimkhani Parisa | ORDOKHANI YADOLLAH | Babolian Esmail | Issue Writer Certificate

Keywords

Fractional Riccati di

erential equation

Fractional-order Bernoulli functions

Caputo derivative

Operational matrix

Collocation method

Abstract

In this paper, a new numerical method for solving the Fractional Riccati di; erential 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.

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APA: Copy

Rahimkhani, Parisa, ORDOKHANI, YADOLLAH, & Babolian, Esmail. (2017). Application of fractional-order Bernoulli functions for solving fractional Riccati di erential equation. INTERNATIONAL JOURNAL OF NONLINEAR ANALYSIS AND APPLICATIONS, 8(2), 277-292. SID. https://sid.ir/paper/340681/en

Vancouver: Copy

Rahimkhani Parisa, ORDOKHANI YADOLLAH, Babolian Esmail. Application of fractional-order Bernoulli functions for solving fractional Riccati di erential equation. INTERNATIONAL JOURNAL OF NONLINEAR ANALYSIS AND APPLICATIONS[Internet]. 2017;8(2):277-292. Available from: https://sid.ir/paper/340681/en

IEEE: Copy

Parisa Rahimkhani, YADOLLAH ORDOKHANI, and Esmail Babolian, “Application of fractional-order Bernoulli functions for solving fractional Riccati di erential equation,” INTERNATIONAL JOURNAL OF NONLINEAR ANALYSIS AND APPLICATIONS, vol. 8, no. 2, pp. 277–292, 2017, [Online]. Available: https://sid.ir/paper/340681/en

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