10.57647/mathsci.2026.2003.89

Advances in Functions Approximation Using Fractional Ruscheweyh Derivative Bases on Multidimensional Hyper-balls

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  • Mohra Zayed*1,
  1. Mathematics Department, College of Science, King Khalid University, Abha 61413, Saudi Arabia

Received: 2026-03-01

Revised: 2026-05-30

Accepted: 2026-06-02

Published in Issue 2026-09-30

Copyright (c) 2026 Mohra Zayed (Author)

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This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Zayed, M. (2026). Advances in Functions Approximation Using Fractional Ruscheweyh Derivative Bases on Multidimensional Hyper-balls. Mathematical Sciences, 20(3). https://doi.org/10.57647/mathsci.2026.2003.89
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Abstract

In this study, the representation of analytic functions in various domains is investigated using multivariable complex conformable fractional Ruscheweyh derivative bases (MCCFRDBs) and multivariable complex con-formable fractional J-integral bases (MCCFJBs) in Fréchet spaces. Specifically, we prove that these represen-tations are valid in closed hyper-balls, open hyper-balls, neighborhoods of closed hyper-balls, neighborhoods of the origin, and spaces of entire functions. Moreover, the order of growth and type of MCCFRDBs and MC-CFJBs are determined, and the T????-property of these bases is investigated. The theoretical results are further illustrated through special cases involving well-known polynomial families, such as hypercomplex proper Bessel polynomials, hypercomplex generalized Bessel polynomials, hypercomplex Bernoulli polynomials, and hypercomplex Euler polynomials. Overall, the findings confirm the general validity of the proposed framework and demonstrate its potential applicability to a broad class of multivariable complex fractional approximation problems.

Keywords

  • Fractional Ruscheweyh derivatives,
  • Fractional integrals,
  • Effectiveness,
  • Growth of bases,
  • Domains of hyper-balls,
  • Fréchet spaces
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