Abstract
In this paper, A new method proposed and coined by the authors as the natural variational iteration transform method(NVITM) is utilized to solve linear and nonlinear systems of fractional differential equations. The new method is a combination of natural transform method and variational iteration method. The solutions of our modeled systems are calculated in the form of convergent power series with easily computable components. The numerical results shows that the approach is easy to implement and accurate when applied to various linear and nonlinear systems of fractional differential equations.
Highlights
The natural transform, initially was defined by Khan and Khan [1] as N - transform, who studied their properties and applications
A novel approach was introduced and utilized to solve linear and nonlinear systems of fractional differential equations. It was emonstrated through different examples how the new method can be used for solving various systems of fractional differential equations
When compared with the existing published methods, it is easy to notice that the new method has many advantages
Summary
The natural transform, initially was defined by Khan and Khan [1] as N - transform, who studied their properties and applications. Later , Belgacem et al [2, 3] defined its inverse and studied some additional fundamental properties of this integral transform and named it the Natural transform. Applications of Natural transform in the solution of differential and integral equations and for the distribution and Bohemians spaces can be found in [3, 4, 5, 6,7, 8,9,10]. We mention the following basic definitions of natural transform
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