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Abstract
In this paper, a new collocation method based on Haar wavelet is developed for numerical solution of Riccati type differential equations with non-integer order. The fractional derivatives are considered in the Caputo sense. The method is applied to one test problem. The maximum absolute estimated error functions are calculated, and the performance of the process is demonstrated by calculating the maximum absolute estimated error functions for a distinct number of nodal points. The results show that the method is applicable and efficient.
Highlights
Fractional differential equations (FDEs) are encountered in model problems in fluid flow, finance, engineering, and other areas of applications [1,2,3,4,5,6,7,8,9,10,11,12]
The proposed numerical method will be developed to find the approximate solution of Riccati type differential equations of fractional order using Haar wavelet collocation method
The Haar wavelet is implemented on the problem which has exact solution
Summary
Fractional differential equations (FDEs) are encountered in model problems in fluid flow, finance, engineering, and other areas of applications [1,2,3,4,5,6,7,8,9,10,11,12]. Fractional Riccati DE (FRDEs) arise in many fields, discussions on the numerical methods for these equations FRDEs are rare. Used the Chebyshev finite difference technique for solution of FRDEs. Li et al [15] used quasi-linearization technique for solution of this problem. Yuzbasi worked on numerical solutions of FRDEs through the Bernstein polynomials [16]. Yuanlu [17] find solution of nonlinear fractional differential equation using
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