Interpretations of some distributional compositions related to Dirac delta function via Fisher's method


ÖZÇAĞ E.

REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, vol.114, no.4, 2020 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 114 Issue: 4
  • Publication Date: 2020
  • Doi Number: 10.1007/s13398-020-00904-5
  • Title of Journal : REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS

Abstract

The powers delta(r) and (delta')(r) of Dirac-delta function and its derivative for arbitrary real number order are recently redefined in distributional sense by means of fractional derivative, [16,23]. In this paper, we define the expression delta(k) (f (x)) for an infinitely differentiable function f (x) having distinct simple roots and k is an element of. N, and furthermore use the double neutrix limit, due to Fisher, of the regular sequences [delta(m)(f (x))(-k)] n to interpret the symbol delta(-k) (f (x)) in which f is an infinitely differentiable function having a simple root.