Abstract
A Legendre wavelet operational matrix method (LWM) is presented for the solution of nonlinear fractional-order Riccati differential equations, having variety of applications in quantum chemistry and quantum mechanics. The fractional-order Riccati differential equations converted into a system of algebraic equations using Legendre wavelet operational matrix. Solutions given by the proposed scheme are more accurate and reliable and they are compared with recently developed numerical, analytical, and stochastic approaches. Comparison shows that the proposed LWM approach has a greater performance and less computational effort for getting accurate solutions. Further existence and uniqueness of the proposed problem are given and moreover the condition of convergence is verified.
Highlights
In recent years, use of fractional-order derivative goes very strongly in engineering and life sciences and in other areas of science
Fractional-order derivatives are used in fruitful way to model many remarkable developments in those areas of science such as quantum chemistry, quantum mechanics, damping laws, rheology, and diffusion processes [1,2,3,4,5] described through the models of fractional differential equations (FDEs)
This paper aims to solve a FDE called fractional-order Riccati differential equation, one of the important equations in the family of FDEs
Summary
Use of fractional-order derivative goes very strongly in engineering and life sciences and in other areas of science. Wavelets theory is one of the growing and predominantly new methods in the area of mathematical and engineering research It has been applied in vast range of engineering sciences; they are used very successfully for waveform representation and segmentations in signal analysis and time-frequency analysis and in the mathematical sciences it is used in thriving manner for solving variety of linear and nonlinear differential and partial differential equations and fast algorithms for easy implementation [23]. The nonlinear Riccati differential equations of fractional-order are approached analytically by using Legendre wavelets method. The Legendre wavelet method (LWM) is illustrated by application, and obtained results are compared with recently proposed method for the fractional-order Riccati differential equation.
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