Analysis of Fractional Nonlinear Differential Equations Using the Homotopy Perturbation Method
نویسندگان
چکیده
In recent years, it has been found that derivatives of non-integer order are very effective for the description of many physical phenomena such as rheology, damping laws, and diffusion processes. These findings invoked the growing interest on studies of the fractal calculus in various fields such as physics, chemistry, and engineering [1 – 4]. In general, there exists no method that yields an exact solution for a fractional differential equation. Only approximate solutions can be derived using the linearization or perturbation methods. Some authors applied the homotopy perturbation method (HPM) [5 – 9], the variational iteration method (VIM) [10 – 12], and the reduced differential transform method [13] to fractional differential equations and revealed that HPM and VIM are alternative analytical methods for solving such type equations. Nobel Laureate Gerardus’t Hooft once remarked that discrete space-time is the most radical and logical viewpoint of reality. Physical phenomena in a fractal spacetime are describable by the fractional calculus [14]. The fractional equations are used to describe discontinuous problems. According to the fractal space-time theory (El Naschie’s e-infinity theory), time and space are discontinuous, and the fractional model is the best candidate to describe such problems [14]. In this paper, we will use HPM for solving time fractional nonlinear fractional differentials. This paper gives an important example of the fractional Kortewegde Vries (KdV) equation, which, according to a re-
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