[PDF] Top 20 A New Modification of the Reconstruction of Variational Iteration Method for Solving Multi-order Fractional Differential Equations

... difference method [10], operational matrix of B-spline functions [11], operational matrix of Legendre polynomials [12,13], operational matrix of Chebyshev polynomials [14], Legendre collocation method [15], ... See full document

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

... approximate fractional differential equations, such as Adomian decomposition method [17], variational iteration method [18], homotopy analysis method [19] and collocation ... See full document

... Non-linear differential equations can model many phenomena in different fields of science and engineering in order to present their behaviors and effects by mathematical ...the equations do ... See full document

... In Section 2, we specify the new iterative equa- tion. The sufficient conditions for convergence of the proposed method are proved in the Section 3. Section 4 includes some numerical examples to show ... See full document

... Following the above steps, we can design a Maple-program which contains three pa- rameters: ICs, Eqs and n. ICs reads the value of initial points. Eqs contains information of the linear terms, the nonlinear terms and the ... See full document

... For illustration purposes, we considered three examples. Results obtained using the scheme presented here agree well with the numerical results presented elsewhere. Results also show that the numerical scheme is very ... See full document

... differential equations, of fractional order and with un- certainty, to consider a new type of dynamical system: fuzzy differential equations of frac- tional order ...tional ... See full document

... Most fractional differential equation don’t have exact analytic solutions , so approximation and numerical techniques must be used ...relatively new approach to provide an analytical approximation to ... See full document

... We can implement the algorithm for solving any example used in this paper. At first call the input numbering to “for-looping”, and then the initial value and value of lambda. Of-course, we need to solve and ... See full document

... accuracy and convergence of the PIM results generally increases when the number of iterations is increased. We can see from table 12 that the error approximation is large for the 2nd and 4th order, but on getting ... See full document

... of variational iteration and Adomian decomposition ...solve fractional diffusion equation. The general equation of fractional diffusion equation is ... See full document

... y  t  y t    y    y   (41) where the last term of right is called “correction”,  n is a general Lagrange multiplier. The above functional is called correction functional, the Lagrange multiplier in the ... See full document

... numerical method relatively new for solving fuzzy fractional differential equations using Adomian decomposition method (ADM) where the fractional derivative is ... See full document

... Fuzzy Fractional Initial Value Problem under Caputo- type fuzzy fractional derivatives by a modified fractional Euler ...merical method for solving FFDE is an area not yet widely ... See full document

... the Variational Iteration Method (VIM) to the system of non-linear differential equations which describe our model and approximating the solutions in a sequence of time ... 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 Variational iteration method was first proposed by He [14–17] and was successfully applied to autonomous ODE in [18], to nonlinear polycrystalline solids [29], and other ...transform ... See full document

... find exact and approximate solutions of linear and nonlinear system of ordinary differential equations. Three numerical examples have been presented to show that this technique is promising. All the ... See full document

... In this paper, a class of tenth-order boundary-value problems is considered. Three examples, solved in [10], are dealt with again to obtain accurate results in the entire domain via the variational ... See full document