Abstract
We propose the variational iteration transform method in the sense of local fractional derivative, which is derived from the coupling method of local fractional variational iteration method and differential transform method. The method reduces the integral calculation of the usual variational iteration computations to more easily handled differential operation. And the technique is more orderly and easier to analyze computing result as compared with the local fractional variational iteration method. Some examples are illustrated to show the feature of the presented technique.
Highlights
Fractional differential equation has been considered with great importance due to its demonstrated applications in various areas such as electrical networks, fluid flow, biology, and dynamical systems [1,2,3,4,5,6,7,8]
We propose the variational iteration transform method in the sense of local fractional derivative, which is derived from the coupling method of local fractional variational iteration method and differential transform method
Local fractional derivative and calculus theory has been introduced by the researcher in [18, 19], which is set up on fractal geometry and which is the best method for describing the nondifferential function defined on Cantor sets
Summary
Fractional differential equation has been considered with great importance due to its demonstrated applications in various areas such as electrical networks, fluid flow, biology, and dynamical systems [1,2,3,4,5,6,7,8]. A great deal of research work has been directed for the nondifferentiable phenomena in fractal domain concerning local fractional derivative, for example, [11, 12, 15, 18,19,20,21,22,23,24,25]. Motivated by the ongoing research method of local fractional differential equation, we present variational iteration transform method, which is the coupling method of local fractional variational iteration method and differential transform method.
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