A generalized Chebyshev wavelet operational matrix (CWOM) is presented for the solution of nonlinear Riccati differential equations. The operational matrix together with suitable collocation points converts the fractional order Riccati differential equations into a system of algebraic equations. Accuracy and efficiency of the proposed method is verified through numerical examples and comparison...

In this paper, a new construction of exact solutions based on the improved generalized Riccati equation mapping method with modified Reimann-Luiviile fractional derivative and symbolic computation is proposed for seeking abundant solutions of the space-time fractional fifth-order nonlinear Sawada-Kotera equation. The proposed method is very simple, direct, effective and convenient for obtaining...

In this paper we utilize the covariance of Riccati equation with respect to linear fractional transformations to define classes of conformally equivalent second order differential equations. This motivates then the introduction of fractional Darboux transformations which can be recognized also as generalized Cole-Hopf transformations. We apply these transformations to find Schrodinger equations...

We consider a nonlinear time fractional partial differential equation with forced term subject to the Neumann boundary condition. Several sufficient conditions are established for oscillation of solutions of such equation by using the integral averaging method and a generalized Riccati technique. The main results are illustrated by examples. 2014 Elsevier Inc. All rights reserved.

The present study introduces a new version of homotopy perturbation method for the solution of system of fractional-order differential equations. In this approach, the solution is considered as a Taylor series expansion that converges rapidly to the nonlinear problem. The systems include fractional-order stiff system, the fractional-order Genesio system, and the fractional-order matrix Riccati-...