2019
DOI: 10.2298/tsci180417118d
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Approximate analytical solutions of non-linear local fractional heat equations

Abstract: Consider the non-linear local fractional heat equation. The fractional complex transform method and the Adomian decomposition method are used to solve the equation. The approximate analytical solutions are obtained.

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Cited by 2 publications
(1 citation statement)
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“…On a smaller scale, for example a scale of water molecule's size, water becomes discontinuous and all laws based on continuous space or continuous time become invalid. Generally we can use Mandelbrot's fractal theory [44] to model the discontinuous phenomena [45][46][47][48][49][50][51][52][53][54][55][56][57][58][59][60]. Newton's calculus is established on an infinitesimal assumption and the function is differentiable, however, the molecule's motion in water at an infinitesimal interval of time or distance is not differentiable.…”
Section: Dimension Is Everything and Two Scale Fractal Geometrymentioning
confidence: 99%
“…On a smaller scale, for example a scale of water molecule's size, water becomes discontinuous and all laws based on continuous space or continuous time become invalid. Generally we can use Mandelbrot's fractal theory [44] to model the discontinuous phenomena [45][46][47][48][49][50][51][52][53][54][55][56][57][58][59][60]. Newton's calculus is established on an infinitesimal assumption and the function is differentiable, however, the molecule's motion in water at an infinitesimal interval of time or distance is not differentiable.…”
Section: Dimension Is Everything and Two Scale Fractal Geometrymentioning
confidence: 99%