The Appell sequences of fractional type

Volume 37, Issue 2, pp 226--235 https://dx.doi.org/10.22436/jmcs.037.02.07

Publication Date: September 25, 2024 Submission Date: May 04, 2024 Revision Date: July 22, 2024 Accteptance Date: August 10, 2024

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Authors

S. Diaz - Departamento de Ciencias Naturales y Exactas, ‎Universidad de la Costa, ‎Barranquilla, ‎Colombia.

Abstract

‎In the article‎, ‎we explore a form of generalization of Appell polynomials stemming from fractional differential operators within the classical sense of Caputo and Riemann-Liuoville‎. ‎To ascertain its generating function‎, ‎we used the Mittag-Leffler function‎. ‎Additionally‎, ‎we propose a determinant form for this novel sequence family and derive general properties thereof‎.

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Keywords

• The Appell polynomials
• Caputo operator
• Riemann-Liouville operator
• Mittag-Leffler function‎

MSC

•  11B83
•  26A33
•  11B68

References

• [1] L. Abadias, P. J. Miana, A subordination principle on Wright functions and regularized resolvent families, J. Funct. Spaces, 2015 (2015), 9 pages
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [2] T. M. Apostol, Introduction to analytic number theory, Springer-Verlag, New York-Heidelberg (1998)
  • View Article
  • Google Scholar


• [3] P. Appell, Sur une classe de polynômes, Ann. Sci. École Norm. Sup. (2), 9 (1880), 119–144
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [4] E. G. Bazhlekova, Subordination principle for fractional evolution equations, Fract. Calc. Appl. Anal., 3 (2000), 213–230
  • View Article
  • Google Scholar
  • MATH


• [5] E. G. Bazhlekova, Fractional evolution equations in Banach spaces, Ph.D Thesis, Eindhoven University of Technology, Eindhoven (2001)
  • View Article
  • Google Scholar


• [6] D. Caratelli, P. Natalini, P. E. Ricci, Fractional Bernoulli and Euler Numbers and Related Fractional Polynomials—A Symmetry in Number Theory, Symmetry, 15 (2023), 13 pages
  • View Article
  • Google Scholar


• [7] I. S. Gradshteyn, I. M. Ryzhik, Table of integrals, series, and products, Elsevier/Academic Press, Amsterdam (2007)
  • View Article
  • Google Scholar
  • MATH


• [8] H. J. Haubold, A. M. Mathai, R. K. Saxena, Mittag-Leffler functions and their applications, J. Appl. Math., 2011 (2011), 51 pages
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [9] N. A. Khan, O. I. Khalaf, C. A. T. Romero, M. Sulaiman, M. A. Bakar, Application of Euler neural networks with soft computing paradigm to solve nonlinear problems arising in heat transfer, Entropy, 23 (2021), 44 pages
  • View Article
  • MathSciNet
  • Google Scholar


• [10] K. S. Miller, B. Ross, An introduction to the fractional calculus and fractional differential equations, John Wiley & Sons, New York (1993)
  • View Article
  • Google Scholar


• [11] S. Nemati, D. F. M. Torres, Application of Bernoulli Polynomials for Solving Variable-Order Fractional Optimal Control- Affine Problems, Axioms, 9 (2020), 18 pages
  • View Article
  • Google Scholar
  • MATH


• [12] J. Peng, K. Li, A note on property of the Mittag-Leffler function, J. Math. Anal. Appl., 370 (2010), 635–638
  • View Article
  • MathSciNet
  • Google Scholar


• [13] P. E. Ricci, R. Srivastava, D. Caratelli, Laguerre-Type Bernoulli and Euler Numbers and Related Fractional Polynomials, Mathematics, 12 (2024), 16 pages
  • View Article
  • Google Scholar