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A fractal interpolation function on a p-series local field Kp is defined, and its p-type smoothness is shown by virtue of the equivalent relationship between the Hölder type space CσKp and the Lipschitz class Lipσ,Kp. The orders of the p-type derivatives and the fractal dimensions of the graphs of Weierstrass type function on local fields are given as an example. The α-fractal function on ℝ is introduced and the conclusion of its smoothness is improved in a more general case; some examples are shown to support the conclusion. Finally, a comparison between the fractal interpolation functions defined on ℝ and Kp is given

discrete dynamics in nature and society

The Smoothness of Fractal Interpolation Functions on<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:mi>ℝ</mml:mi></mml:mrow></mml:math>and on<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:math>-Series Local Fields

The Smoothness of Fractal Interpolation Functions onℝand onp-Series Local Fields