Published Online: 24 July 2019
AIP Conference Proceedings 2116, 160004 (2019); https://doi.org/10.1063/1.5114148
We present a generalization of several results of the classical continuous Clifford function theory to the context of fractional Clifford analysis. The aim of this paper is to show how the fractional integro-differential hypercomplex operator calculus can be applied to a concrete fractional Stokes problem in arbitrary dimensions which has been attracting recent interest (cf. [1, 6]).
  1. 1. P.M. de Carvalho-Neto and G. Planas, Mild solutions to the time fractional Navier-Stokes equations inn, J. Differ. Equations, 259-No. 7, (2015), 2948–2980. https://doi.org/10.1016/j.jde.2015.04.008, Google ScholarCrossref
  2. 2. M. Ferreira, R.S. Kraußhar, M.M. Rodrigues and N. Vieira; A higher dimensional fractional Borel-Pompeiu formula and a related hypercomplex fractional operator calculus, submitted. Google Scholar
  3. 3. R. Gorenflo, A.A. Kilbas, F. Mainardi and S. Rogosin, Mittag-Leffler functions. Theory and applications, Springer Monographs in Mathematics, Springer, Berlin, 2014. Google Scholar
  4. 4. K. Gürlebeck and W. Sprößig, Quaternionic and Clifford calculus for physicists and engineers, Mathematical Methods in Practice, Wiley, Chichester, 1997. Google Scholar
  5. 5. A.A. Kilbas, H.M. Srivastava and J.J. Trujillo, Theory and applications of fractional differential equations, orth-Holland Mathematics Studies Vol. 204, Elsevier, Amsterdam, 2006. Google Scholar
  6. 6. S. Lin, M. Azaïez and C. Xu, Fractional Stokes equation and its spectral approximation, Int. J. Numer. Anal. Model., 15-No. 1-2, (2018), 170–192. Google Scholar
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