UNIFORM CONTINUITY OF FRACTIONAL ORDER INTEGRAL OF FRACTAL INTERPOLATION FUNCTION

Xuezai Pan and Xudong Shang
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Xuezai Pan: School of Mathematics and Physics, Yancheng Institute of Technology, Yancheng, Jiangsu 224003, P. R. China
Xudong Shang: ��School of Mathematics, Nanjing Normal University, Taizhou College, Taizhou 225300, P. R. China

FRACTALS (fractals), 2022, vol. 30, issue 06, 1-7

Abstract: It is the purpose of this paper that uniform continuity of fractional order integral of fractal interpolation function (FIF) is researched. First, FIF generated by affine transformation is constructed. Second, the combination between Riemann–Liouville fractional order integral and FIF is defined. Finally, the continuity and the uniform continuity of fractional order integral of FIF are proved by compactness theorem of numbers sequence or finite covering theorem. The result shows that fractional order integral of FIF is uniformly continuous on a closed interval.

Keywords: Fractal Geometry; Fractional Order Integral; Affine Mapping; Fractal Interpolation Function; Uniform Continuity (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X22501250

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