An efficient new iterative method for finding exact solutions of nonlinear time-fractional partial differential equations

In recent years, notable contributions have been made to both the theory and applications of the fractional differential equations. These equations are increasingly used to model problems in research areas as diverse as population dynamics, mechanical systems, fiber optics, control, chaos, fluid mechanics, continuous-time random walks, anomalous diffusive and subdiffusive systems, unification of diffusion and wave propagation phenomenon, dynamical systems and others. The most important advantage of using fractional differential equations in these and other applications is their non-local property. It is well known that the integer order differential operator is a local operator but the fractional order differential operator is non-local. This means that the next state of a system depends not only upon its current state but also upon all of its historical states. This is more realistic and it is one reason why fractional calculus [1–4] has become more and more popular. In general, there exists no method that yields an exact solution for a fractional differential equation. Approximation and numerical solutions are used extensively [5–10]. In the present paper, we use new iterative method (NIM) to construct an exact solution