Skip Navigation Links
Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

Email: dumitru.baleanu@gmail.com


A New Local Fractional Derivative of q−uniform Type

Discontinuity, Nonlinearity, and Complexity 8(1) (2019) 101--109 | DOI:10.5890/DNC.2019.03.009

Juan E. Nápoles Valdes, Jorge A. Castillo Medina, Paulo M. Guzmán, Luciano Miguel Lugo

UNNE, FaCENA, Corrientes, Argentina, UTN, FRRE, Resistencia, Chaco, Argentina

Download Full Text PDF

 

Abstract

In this work we present a new derivative of q-uniform type, which contains several definitions of known q-derivatives. Some examples and properties similar to those of the ordinary calculus are also presented.

References

  1. [1]  Victor, K. and Cheung, P. (2002), Quantum Calculus, Springer-Verlag.
  2. [2]  Jackson, F.H. (1908), On q-functions and a certain difference operator, Trans. Roy. Soc. Edin., 46, 253-281.
  3. [3]  Jackson, F.H. (1910), On q-definite integrals, Quart. J. Pure and Appl. Math., 41, 193-203.
  4. [4]  Finkelstein, R.J. (1996), The q-Coulomb problem, J. Math. Phys., 37(6), 2628-2636.
  5. [5]  Finkelstein, R.J. (1967), Symmetry group of the hydrogen atom, J. Math. Phys., 8(3), 443-449.
  6. [6]  Ernst, T. (2001), The history of q?calculus and a new method, thesis, Uppsala, University.
  7. [7]  Neamaty, A. and Tourani, M. (2017), The presentation of a new type of quamtun calculus, Tbilisi Math. J., 10(2), 15-28.
  8. [8]  Aldwoah, K.A., Malinowska, A.B., and Torres, DS.F.M. (2012), The power quantum calculus and variational problems, Dynamic of Continuous, Discrete and Impulsive Systems, Serie B: Applications & Algoriths, 19, 93-116.
  9. [9]  Vanterler Da C., Sousa, J., de Oliveira, E.C. (2017), On the local m-derivative, ArXiv:1704.08186v3.
  10. [10]  Hamza, A.E., Sarhan, A.S.M., Shehata, E.M., and Aldwoah, K.A. (2015), A general quantum difference calculus, Advances in Difference Equations, 182, 19 p.
  11. [11]  Liénard, A. (1928), Étude des oscillations entretenues, Revue Génerale de l' Électricité 23, 901-912, 946-954.
  12. [12]  Guckenheimer, J. and Holmes, P. (2002), "Nonlinear oscillations, dynamical systems, and bifurcations of vector fields", volume 42 of Applied Mathematical Sciences. Springer-Verlag, New York. Revised and corrected reprint of the 1983 original.
  13. [13]  Van der Pol, B. (1922), On oscillation hysteresis in a triode generator with two degrees of freedom, Phil. Mag (6) 43, 700-719.
  14. [14]  Van der Pol, B. (1926), On "relaxation-oscillations", Philosophical Magazine, 2(11), 978-992.
  15. [15]  Li, Y., Chen, Y.Q., and Podlubny, I. (2010), Stability of fractional-order nonlinear dynamic systems: Lyapunov direct method and generalized Mittag Leffler stability, Comput. Math. Appl., 59, 1810-1821.