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<p>A novel class of bivariate <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\alpha \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation>-fractal functions is constructed on rectangular grids in this paper, with sufficient conditions established for these <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\alpha \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation>-fractal functions to become <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\alpha \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation>-fractal interpolation functions (<InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(\alpha \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation>-FIFs). The box-counting dimension of the resulting <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(\alpha \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation>-FIFs is subsequently estimated. Three numerical examples are provided to illustrate the effectiveness and practical applicability of the proposed construction method. Finally, it is demonstrated that the Riemann-Liouville fractional integrals of the constructed bivariate <InlineEquation ID="IEq8"> <EquationSource Format="TEX">\(\alpha \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation>-fractal functions remain <InlineEquation ID="IEq9"> <EquationSource Format="TEX">\(\alpha \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation>-fractal functions.</p>

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A novel class of bivariate \(\alpha \)-fractal functions and their fractional integrals

  • 期刊论文

  • 发表日期：

    2026年2月2日

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  • Wen-Jie Cai,
  • Hong-Yong Wang

摘要

A novel class of bivariate \(\alpha \) α -fractal functions is constructed on rectangular grids in this paper, with sufficient conditions established for these \(\alpha \) α -fractal functions to become \(\alpha \) α -fractal interpolation functions ( \(\alpha \) α -FIFs). The box-counting dimension of the resulting \(\alpha \) α -FIFs is subsequently estimated. Three numerical examples are provided to illustrate the effectiveness and practical applicability of the proposed construction method. Finally, it is demonstrated that the Riemann-Liouville fractional integrals of the constructed bivariate \(\alpha \) α -fractal functions remain \(\alpha \) α -fractal functions.