[PDF] Top 20 A semi analytic method with an effect of memory for solving fractional differential equations

... 61:2528-2534, 2011; Gökdo ˘gan et al. in Math. Comput. Model. 54:2132-2138, 2011), authors have updated an initial condition in each sub-domain by using the approximate solution in the previous sub-domain. However, we ... See full document

... differential equations have gained considerable importance due to their frequent applications in various fields of science and engineering [1-2], integral equa- tions [3], viscoelastic damping materials [4-5], ... See full document

... decades, fractional differential equations have been paid an increasing attention as they are widely used to describe various complex phenomena in many fields such as the fluid flow, signal processing, control ... See full document

... Partial Differential Equations have remarkable developments in different areas like gravitation, chemical reaction, fluid dynamics, dispersion, nonlinear optics, plasma physics, acoustics ...wave ... See full document

... collocation method is proposed for solving linear and nonlinear multi-order fractional differential equations based on the new definition of fractional derivative which is ... See full document

... by fractional differential and integral equations, and finding the solu- tions of these equations has been the subject of many investigators in recent ...perturbation method (HPM) [], the ... See full document

... the memory and non-local characters of frac- tional derivative, many scholars use fractional differential equations to simulate complex phenomenon in order to make it closer to the real ...of ... See full document

... Traditional and new integral transform methods have been applied to find the analytical solution of FDE. Some of them are Laplace, Mellin, Fourier, Sumudu, Natural, Elzaki and Kamal [2-8]. Many researchers have shown ... See full document

... differential equations. Among these are the variational iteration method [– ], the Adomian descomposition method [, ], the fractional sub-equation method [–], the homotopy ... See full document

... the fractional partial differential equations are defined by modified Riemann-Liouville fractional ...of fractional derivative and fractional complex transform, these equations can ... See full document

... ordinary differential zzy fractional differential equation (FFDE) is equation to arbitrary non-integer ...fuzzy fractional differential equations in [2, ...for solving ... See full document

... Physics Fractional calculus is found to be more suitable modeling the process with long range interaction and physical problems described by fractional equations, but sometimes it’s difficult to get ... See full document

... decomposition method was first applied in [4]. It is a numerical method based on the Taylor series expansion which constructs an analytical solution in the form of a ...this method, one obtains a ... See full document

... decades differential equations involving fractional derivatives and integrals have been studied by many ...phenomena, fractional partial differential equations have been used in ... See full document

... new fractional sub-equation method is proposed for finding exact solutions of fractional partial differential equations (FPDEs) in the sense of modi- fied Riemann-Liouville ... See full document

... One of the well known class of polynomials frequently used in literature is the class of Bernstein polynomials. These polynomials are not orthogonal but they have certain properties which makes them applicable to ... See full document

... In this work, we proposed an algorithm for solving the nonlinear equations. We derived analytically the order of convergence of this algorithm, which is P = 7. According to obtained results, the iterative ... See full document

... approximation method for solving linear and nonlinear problems and at beginning it was proposed for solving nonlinear fractional differential equations [6], by modifying He’s ... See full document

... In this paper, we investigated on functional Hammerstein integro-differential equa- tions of fractional order. Here we also presented an approximate method to solve these equations. We proved ... See full document

... ble 1. Figure 1 presents the agreement between the exact and the approximate solutions in Example 2 for different choices of γ . From the numerical results, we see that the pro- posed method gives accurate results. ... See full document