Abstract:
A Legendre wavelet operational matrix method (LWM) presented for the solution of nonlinear fractional order Riccati differential equations, having variety of applications in engineering and applied science. 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.
Keywords: Fractional Calculus, Fractional order Riccati differential equation, Solution, Solving fractional differential equations, Legendre wavelet, Riemann -Liouville fractional derivative, Caputo fractional derivative.