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Fractional Calculus of Fractal Interpolation Function on

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  • XueZai Pan

Abstract

The paper researches the continuity of fractal interpolation function’s fractional order integral on and judges whether fractional order integral of fractal interpolation function is still a fractal interpolation function on or not. Relevant theorems of iterated function system and Riemann-Liouville fractional order calculus are used to prove the above researched content. The conclusion indicates that fractional order integral of fractal interpolation function is a continuous function on and fractional order integral of fractal interpolation is still a fractal interpolation function on the interval .

Suggested Citation

  • XueZai Pan, 2014. "Fractional Calculus of Fractal Interpolation Function on," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-5, April.
    • Handle: RePEc:hin:jnlaaa:640628
    DOI: 10.1155/2014/640628
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    Cited by:

    1. Ri, Mi-Gyong & Yun, Chol-Hui, 2020. "Riemann Liouville fractional integral of hidden variable fractal interpolation function," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    2. Prasad, S.A. & Verma, S., 2023. "Fractal interpolation function on products of the Sierpiński gaskets," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    3. Ri, Mi-Gyong & Yun, Chol-Hui & Kim, Myong-Hun, 2021. "Construction of cubic spline hidden variable recurrent fractal interpolation function and its fractional calculus," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).

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