scholarly journals Solution of Scalar Riccati Differential Equation of Fractional Order

2019 ◽  
Vol 22 (4) ◽  
pp. 68-74
Author(s):  
Fadhel Subhi Fadhel ◽  
◽  
Sabreen Hashim Jasim ◽  
Keyword(s):  
Differential Equation ◽  
Fractional Order ◽  
Riccati Differential Equation

scholarly journals Application of Generalized Differential Transform Method to Special Cases of Riccati Differential Equation of Fractional Order

2019 ◽  
Vol 8 (3) ◽  
pp. 2774-2779
Keyword(s):  
Differential Equation ◽  
Numerical Solution ◽  
Fractional Order ◽  
Fractional Derivatives ◽  
Differential Transform Method ◽  
Riccati Differential Equation ◽  
Transform Method ◽  
Special Cases ◽  
Differential Transform ◽  
Generalized Differential

In this paper, we acquire the inexact solutions of Special cases of Riccati Differential equation of Fractional order using Generalized Differential Transform Method (GDTM). The fractional derivatives are described in the Caputo sense. Accuracy and competence of the proposed method is verified through numerical solution of some special cases of Riccati Differential equation of fractional order. The obtained results reveal that the performance of the proposed method is specific and predictable.

Fractional-order generalized Legendre wavelets and their applications to fractional Riccati differential equations

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Boonrod Yuttanan ◽  
Mohsen Razzaghi ◽  
Thieu N. Vo
Keyword(s):  
Differential Equation ◽  
Fractional Order ◽  
Algebraic System ◽  
Fractional Integral ◽  
Exact Formula ◽  
Legendre Wavelets ◽  
Riccati Differential Equation ◽  
Numerical Examples ◽  
Riccati Differential Equations ◽  
The Given

Abstract In the present paper, fractional-order generalized Legendre wavelets (FOGLWs) are introduced. We apply the FOGLWs for solving fractional Riccati differential equation. By using the hypergeometric function, we obtain an exact formula for the Riemann–Liouville fractional integral operator (RLFIO) of the FOGLWs. By using this exact formula and the properties of the FOGLWs, we reduce the solution of the fractional Riccati differential equation to the solution of an algebraic system. This algebraic system can be solved effectively. This method gives very accurate results. The given numerical examples support this claim.

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