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

ÖZÇAĞ, EMİN

doi:10.1007/s13398-020-00904-5

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

REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, cilt.114, sa.4, 2020 (SCI-Expanded)

Yayın Türü: Makale / Tam Makale
Cilt numarası: 114 Sayı: 4
Basım Tarihi: 2020
Doi Numarası: 10.1007/s13398-020-00904-5
Dergi Adı: REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS
Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, Communication Abstracts, MathSciNet, zbMATH, DIALNET, Civil Engineering Abstracts
Hacettepe Üniversitesi Adresli: Evet

Özet

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.