Abstract
The local fractional Poisson equations in two independent variables that appear in mathematical physics involving the local fractional derivatives are investigated in this paper. The approximate solutions with the nondifferentiable functions are obtained by using the local fractional variational iteration method.
Highlights
As it is known the Poisson equation plays an important role in mathematical physics [1, 2]; that is, it describes the electrodynamics and intersecting interface
The local fractional derivative of f(x) of order α is defined as dαf (x0) dxα
The formulas of local fractional derivatives of special functions [37] used in the paper are as follows: dα dxα xnα Γ (1 + nα) x(n−1)α + (n − 1)
Summary
As it is known the Poisson equation plays an important role in mathematical physics [1, 2]; that is, it describes the electrodynamics and intersecting interface (see, e.g., [3, 4] and the cited references therein) The solution of this equation was discussed by using different methods [5–9]. The local fractional variational iteration method, initiated in [32], was used to find the nondifferentiable solutions for the heat-conduction [32], Laplace [33], damped and dissipative wave [34], Helmholtz [35] and Fokker-Planck [36] equations, the wave equation on Cantor sets [37], and the fractal heat transfer in silk cocoon hierarchy [38] with local fractional derivative. The formulas of local fractional integrals of special functions used in the paper are presented as follows [37]: 0Ix(α) ag (x) = a 0Ix(α) g (x) , 0It(α). N ∈ N, where g(x) is a local fractional continuous function, a is a constant, and N is a set of positive integers
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