Some New Results in the $q-$Calculus

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Authors

  • Jorge A. Castillo Medina Author
  • Salvador Cruz García Author
  • Juan E. Nápoles Valdes Author
  • Thelma Galeana Moyaho Author

Correspondence: Jorge A. Castillo Medina jcastillo7701@gmail.com

DOI:

https://doi.org/10.5890/DNC.2021.12.014

Abstract

In this paper, we present some results for a fractional derivative of type $q$ uniform defined by the authors in a previous work, and which are generalizations of known classical results of ordinary calculus.

References

[1] Kac, V. and Cheung, P. (2002), Quantum Calculus, Springer-Verlag.

[2] Nápoles, V., Castillo Medina, J.A., Guzmán, P.M., and Lugo, L.M. (2019), A new local fractional derivative of q-uniform type, Discontinuity, Nonlinearity, and Complexity, 8(1), 101-109.

[3] Mercer, P.R. (2002), On A Mean Value Theorem, The College Mathematics Journal, 33(1), 46-48. JSTOR, www.jstor.org/stable/1558980. DOI:10.2307/1558980.

[4] Rajkovic, P., Stankovic, M., and Marinkovic, S. (2002), Mean Value Theorems in q-calculus, Matematicki Vesnik, 54(219), 171-178.

[5] Tong, J. (1999), The mean value theorems of Lagrange and Cauchy, Int. J. Math. Educ. Sci. Technol., 30, 456-458.

[6] Tong, J. (2000), The mean value theorems of Lagrange and Cauchy (II), Int. J. Math. Educ. Sci. Technol., 31(3), 447-449.

[7] Bosch, P., Gomez-Aguilar, J.F., Rodriguez, J.M., and Sigarreta, J.M. (2020), Analysis of Dengue fever outbreak by generalized fractional derivative, Fractals, 28(8), DOI:10.1142/S0218348X20400381.

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PublishedDecember 2021

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How to Cite

Medina, J. A. C., García, S. C., Valdes, J. E. N., & Moyaho, T. G. (2021). Some New Results in the $q-$Calculus. Discontinuity, Nonlinearity, and Complexity, 10(4), 755-763. https://doi.org/10.5890/DNC.2021.12.014