On Some Extended Results in Functional \(q(t)\)-Calculus: Theoretical and Numerical Applications

Authors

  • S. S. Manjarekar Department of Mathematics and Research, L. V. H. ASC College (Autonomous) (affiliated to Savitribai Phule Pune University), Panchavati, Nashik 422003, Maharashtra, India https://orcid.org/0009-0006-9411-355X
  • V. R. Nikam Department of Mathematics and Research, L. V. H. ASC College (Autonomous) (affiliated to Savitribai Phule Pune University), Panchavati, Nashik 422003, Maharashtra, India

DOI:

https://doi.org/10.26713/cma.v16i3.3269

Keywords:

q- calculus, q - Identities, Hypergeometric functions, Quantum calculus

Abstract

This paper provides further applications of a functional approach to quantum calculus, towards functional \(q(t)\)-integral, functional \(q(t)\)-Taylor’s formula difference equations with variable coefficients together with functional quantum congruence theory.

Downloads

Download data is not yet available.

References

W. A. Al-Salam, q-Bernoulli numbers and polynomials, Mathematische Nachrichten 17(3-6) (1958), 239 – 260, DOI: 10.1002/mana.19580170311.

T. M. Apostol, Introduction to Analytic Number Theory, 1st edition, Undergraduate Texts in Mathematics series, Springer, New York, NY, xii + 340 pages (1976), DOI: 10.1007/978-1-4757-5579-4.

W. N. Bailey, Hypergeometric Series, Reprinted by Hafner, New York, (1972).

T. Ernst, A New Method for q-Calculus, Dissertations, Department of Mathematics, Uppsala University, Sweden (2002), URL: https://solnaschack.org/ernst/index.html.

T. Ernst, A New Notation for q-Calculus and a New q-Taylor Formula, U.U.D.M. Report 1999:25, ISSN 1101-3591, Department of Mathematics, Uppsala University, (1999).

T. Ernst, The History of q-Calculus and a New Method, U.U.D.M. Report 2000:16, Department of Mathematics, Uppsala University, Sweden (2000).

T. Ernst, A method for q-Calculus, Journal of Nonlinear Mathematical Physics 10(4) (2003), 487 – 525, DOI: 10.2991/jnmp.2003.10.4.5.

H. Jafari and S. Manjarekar, A new concept of q-Calculus with respect to another function, Journal of Innovative Applied Mathematics and Computational Sciences 4(2) (2024), 113 – 121, URL: https://jiamcs.centre-univ-mila.dz/index.php/jiamcs/article/view/v4i2.

V. Kac and P. Cheung, Quantum Calculus, Universitext series, Springer-Verlag, New York, ix + 112 pages (2002), DOI: 10.1007/978-1-4613-0071-7.

B. A. Kupershmidt, q-Newton binomial: From Euler to Gauss, Journal of Nonlinear Mathematical Physics 7(2) (2000), 244 – 262, DOI: 10.2991/jnmp.2000.7.2.11.

N. N. Lebedev, Special Functions and Their Applications, Prentice-Hall, Inc., Englewood Cliffs, N.J., xii + 308 pages (1965).

P. Podle´s and E. Müller, Introduction to quantum groups, Reviews in Mathematical Physics 10(04) (1998), 511 – 551, DOI: 10.1142/S0129055X98000173.

E. D. Rainville, Special Functions, Chelsea Publishing Company, Bronx, New York, 365 pages (1971).

A. C. Sparavigna, The q-integers and the Mersenne numbers, SSRN Electronic Journal 2018 (2018), 10 pages, DOI: 10.2139/ssrn.3183800.

J. Tariboon, S. K. Ntouyas and P. Agarwal, New concepts of fractional quantum calculus and applications to impulsive fractional q-difference equations, Advances

Downloads

Published

30-10-2025
CITATION

How to Cite

Manjarekar, S. S., & Nikam, V. R. (2025). On Some Extended Results in Functional \(q(t)\)-Calculus: Theoretical and Numerical Applications. Communications in Mathematics and Applications, 16(3), 831–844. https://doi.org/10.26713/cma.v16i3.3269

Issue

Vol. 16 No. 3 (2025)

Section

Research Article

License

Creative Commons Licence 4.0 by  

Authors who publish with this journal agree to the following terms:

  • Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a CCAL that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
  • Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
  • Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.