[PDF] Top 20 Homotpy Analysis Method for Solving Fractional Differential Equations

... expansion method that is not directly dependent on small or large physical ...unified method for the Lyapunov artificial small parameter method, the delta expansion method, the Adomian ... See full document

... differential equations are generalizations of differential equations of inte- ger ...nonlinear fractional differential equations (FDEs) have gained importance and popularity in various fields of ... See full document

... Decomposition Method [1, 2] has been applied to obtain a formal solution to a wide class of both deterministic and stochastic Partial Differential ...this Method has emerged as an alternative ... See full document

... the fractional power series are generalized for the fuzzy frac- tional power series by using fuzzy Caputo deriva- ...fuzzy fractional power series to solve the fractional differential ... See full document

... the fractional calculus gets involved in more and more areas, especially in control theory – viscoelastic, theory-electronic, chemicals -fractal theory and so ...for fractional differential ... See full document

... for solving differential equations of fractional order, such as Lie group method, invariant subspace method and numerical methods, [1, 2, 3, ...the method of ... See full document

... all coefficients in Taylor series can be determined by solving the recursive equation that is induced from the given differential equation. In order to apply the DTM to solve frac- tional problems, we adopt the ... See full document

... where the contained fractional derivative is the modified Riemann-Liouville derivative. The corresponding integer order equation to () can be found in [, ]. Now we will apply the described method in ... See full document

... Decomposition Method (ADM) [2, 19, 20], Variational Iteration Method (VIM) [11, 20], Homotopy Perturbation Method (HPM) [9], and EXP-function Method [24] see also [12– 14, ...to solving ... See full document

... homotopy analysis method which is based on homotopy analysis method and Laplace transform is used to solve the system of partial differential equations of fractional ... See full document

... Generalized Differential Transformation Method (GDTM) for approximating the solution of systems of linear volterra integro-differential equations of fractional of fractional is ... See full document

... of fractional orthogonal polynomials and solving the fractional neutral pantograph delay differential equations by the obtained operational ...suitable fractional orthogonal polynomials ... See full document

... wavelet method is presented for solving Riccati differential ...of fractional integration is derived and utilized to transform the equations to system of algebraic ...error analysis of ... See full document

... where a and b are arbitrary constants. It arises as a description of gravity water waves in the long-wave regime. Using the traveling wave transformation u(x, t) = U(ξ), where ξ = kx + ct and k, c are non zero constants, ... See full document

... of fractional partial differential equations (FPDE's) in finance, physics, image processing and engineering [1, ...partial differential equations ...general method that can be ... See full document

... about fractional derivative and fractional integral which will be used in the following ...decomposition method, and the detailed Scheme about the time fractional differential Equation ... See full document

... Lu+Ru+Nu=g (3.1) where L is the highest order derivative which is assumed to be easily invertible, R is a linear differential operator of order less than L, N represents the nonlinear terms, and g is the source ... See full document

... numerical method for solving fuzzy differential equation of fractional order under gH-fractional Caputo ...this method is to approximate the solution of fuzzy fractional ... 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

... Existence and uniqueness of solution of fractional differ- ential equations (1) for a given initial condition (2) have been proven in [8], (see also [10, (Sect.2)]). It is shown [13, (theorem 1, section ... See full document