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.