638
Views
0
CrossRef citations to date
0
Altmetric
Research Article

New definitions of fractional derivatives and integrals for complex analytic functions

ORCID Icon & ORCID Icon
Pages 675-690 | Received 26 Jun 2023, Accepted 05 Nov 2023, Published online: 15 Nov 2023

References

  • Abdelhakim, A. A. (2019). The flaw in the conformable calculus: It is conformable because it is not fractional. Fractional Calculus and Applied Analysis, 22(2), 242–254. doi:10.1515/fca-2019-0016
  • Abdelhakim, A. A., & Machado, J. A. T. (2019). A critical analysis of the conformable derivative. Nonlinear Dynamics, 95(4), 3063–3073. doi:10.1007/s11071-018-04741-5
  • Abu Ghuwaleh, M., Saadeh, R., & Burqan, A. (2022). New theorems in solving families of improper integrals. Axioms, 11(7), 301. doi:10.3390/axioms11070301
  • Abu-Ghuwaleh, M., Saadeh, R., & Qazza, A. (2022a). A novel approach in solving improper integrals. Axioms, 11(10), 572. doi:10.3390/axioms11100572
  • Abu-Ghuwaleh, M., Saadeh, R., & Qazza, A. (2022b). General master theorems of integrals with applications. Mathematics, 10(19), 3547. doi:10.3390/math10193547
  • Ahlfors, L. V. (1979). Complex analysis: An introduction to the theory of analytic functions of one complex variable. New York, NY: McGraw-Hill Book Co.
  • Bhrawy, A. H., Taha, T. M., & Machado, J. A. T. (2015). A review of operational matrices and spectral techniques for fractional calculus. Nonlinear Dynamics, 81(3), 1023–1052. doi:10.1007/s11071-015-2087-0
  • Bohnenblust, H. F., & Hille, E. (1931). On the absolute convergence of Dirichlet series. The Annals of Mathematics, 32(3), 600–622. doi:10.2307/1968420
  • Carpinteri, A., & Fabrizio, A. (Eds.). (n.d.). Fractional calculus and its applications in physics.
  • Churchill, R. V. (1974). Complex variables and applications. New York, NY: McGraw-Hill Book Co.
  • Fernandez, A., & Husain, I. (2020). Modified Mittag-Leffler functions with applications in complex formulae for fractional calculus. Fractal and Fractional, 4(3), 45. doi:10.3390/fractalfract4030045
  • Hilfer, R. (n.d.). Fractional calculus: Theory and applications of differentiation and integration to arbitrary order.
  • Jiang, Y., & Zhang, B. (2020). Comparative study of Riemann–Liouville and Caputo derivative definitions in time-domain analysis of fractional-order capacitor. IEEE Transactions on Circuits and Systems II: Express Briefs, 67(10), 2184–2188. doi:10.1109/TCSII.2019.2952693
  • Li, C., Qian, D., & Chen, Y. Q. (2011). On Riemann-Liouville and Caputo derivatives. Discrete Dynamics in Nature and Society, 2011, 1–15. Article ID 562494. doi:10.1155/2011/562494
  • Meerschaert, M. M., & Sikorskii, A. (n.d.). Fractional calculus: An introduction for physicists.
  • Miller, K. S. (1993). An introduction to fractional calculus and fractional differential equations. New York, NY: J. Wiley and Sons.
  • Moshrefi-Torbati, M., & Hammond, J. K. (1998). Physical and geometrical interpretation of fractional operators. Journal of the Franklin Institute, 335(6), 1077–1086. doi:10.1016/S0016-0032(97)00048-3
  • Oldham, K. B., & Spanier, J. (n.d.). An introduction to fractional calculus and fractional differential equations.
  • Oldham, K., & Spanier, J. (1974). The fractional calculus: Theory and applications of differentiation and integration of arbitrary order. USA: Academic Press.
  • Podlubny, I. (1999). Fractional differential equations: An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications. San Diego, CA: Academic Press.
  • Rudin, W. (1987). Real and complex analysis. New York, NY: McGraw-Hill Book Co.
  • Saadeh, R., Abu-Ghuwaleh, M., Qazza, A., & Kuffi, E. (2022). A fundamental criteria to establish general formulas of integrals. Journal of Applied Mathematics, 2022, 1–16, Article 6049367. doi:10.1155/2022/6049367
  • Sabatier, J., Agrawal, O. P., & Tenreiro Machado, J. A. (Eds.) (n.d.). Fractional calculus and its applications.
  • Samko, S., Kilbas, A., & Marichev, O. (n.d.). Fractional differentiation and integration: Theory and applications.
  • Trujillo, J. J., & Rubio, J. L. (Eds.). (n.d.-a). Fractional calculus in bioengineering.
  • Trujillo, J. J., & Rubio, J. L. (Eds.). (n.d.-b). Fractional differentiation and its real world applications.
  • Zwillinger, D. (2014). Table of integrals, series, and products. San Diego, CA: Academic Press.