An exponential spline for solving the fractional riccati differential equation

Authors
reza jalilian 1
hooman emadifar 2
1 Department of Mathematics, Faculty of Basic Sciences, Razi University, Kermanshah, Iran.
2 Department of Mathematics, Faculty of Basic Sciences, Islamic Azad University, Hamedan, Iran.
Abstract
In this Article, proposes an approximation for the solution of the Riccati equation based on the use of exponential spline functions. Then the exponential spline equations are obtained and the differential equation of the fractional Riccati is discretized. The effect of performing this mathematical operation is obtained from an algebraic system of equations. To illustrate the benefits of the method proposed here the error analysis and convergence article are also discussed based on this exponential spline. Finally, a second-order method is obtained. One of the benefits of this proposed method is that it is not only for solving fractional Riccati equations, but also for a variety of Fractional equations that can be used. To illustrate the effectiveness of this method by solving numerical examples and a comparison of the results obtained from the implementation of this proposed method with the results of other existing numerical methods proves the claim that the proposed method is a good approximation for the fractional Riccati equations.
Keywords
Fractional riccati differential equation
Caputo derivative
Exponential Spline
Convergence
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