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NEW FRACTIONAL DERIVATIVE IN COLOMBEAU ALGEBRA

Yıl 2018, Cilt: 1 Sayı: 2, 180 - 189, 31.07.2018

Öz

In this paper we introduce an approach to fractional derivatives involving singularities based on the theory of algebras of generalized functions in the Colombeau algebra G, using new denition of fractional derivative called conformable fractional derivative introduced by the authors Khalil et al. in ([8]).

Kaynakça

  • J. F. Colombeau, Elementary Introduction in New Generalized Functions, North Holland, Amsterdam, 1985.
  • M. Stojanovic, Fondation of the fractional calculus in generalized function algebras, Analysis And Applications, Vol. 10 No. 4, 439--467 (2012).
  • M. Oberguggenberger, Generalized functions in nonlinear models a survey, Nonlinear Analysis 47, 5040--5049 (2001).
  • D. Rajterc Ciric And M. Stojanovic, Fractional derivatives of multidimensional Colombeau generalized stochastic processes ,Fract. Calc. Appl. Anal., Vol. 16 No 4, 949--961 (2013)
  • D. Rajterc Ciric and M. Stojanovic, Convolution-type derivatives and transforms of Colombeau generalized stochastic processes, Integral Transforms Spec. Funct. 22 (4-5), 319--326 (2011).
  • D. Rajter-Ciric, A note on fractional derivatives of Colombeau generalized stochastic processes, Novi Sad J. Math. 40, No 1, 111--121 (2010).
  • R. Khalil, M. Al Horani, A. Yousef, And M. Sababheh, A new definition of fractional derivative, J. Comput. Appl. Math. 264, 65--70 (2014).
  • T. Abdeljawad, On conformable fractional calculus, J. Comput. Appl. Math. Vol. 279 (C), 57--66 (2015).
Yıl 2018, Cilt: 1 Sayı: 2, 180 - 189, 31.07.2018

Öz

Kaynakça

  • J. F. Colombeau, Elementary Introduction in New Generalized Functions, North Holland, Amsterdam, 1985.
  • M. Stojanovic, Fondation of the fractional calculus in generalized function algebras, Analysis And Applications, Vol. 10 No. 4, 439--467 (2012).
  • M. Oberguggenberger, Generalized functions in nonlinear models a survey, Nonlinear Analysis 47, 5040--5049 (2001).
  • D. Rajterc Ciric And M. Stojanovic, Fractional derivatives of multidimensional Colombeau generalized stochastic processes ,Fract. Calc. Appl. Anal., Vol. 16 No 4, 949--961 (2013)
  • D. Rajterc Ciric and M. Stojanovic, Convolution-type derivatives and transforms of Colombeau generalized stochastic processes, Integral Transforms Spec. Funct. 22 (4-5), 319--326 (2011).
  • D. Rajter-Ciric, A note on fractional derivatives of Colombeau generalized stochastic processes, Novi Sad J. Math. 40, No 1, 111--121 (2010).
  • R. Khalil, M. Al Horani, A. Yousef, And M. Sababheh, A new definition of fractional derivative, J. Comput. Appl. Math. 264, 65--70 (2014).
  • T. Abdeljawad, On conformable fractional calculus, J. Comput. Appl. Math. Vol. 279 (C), 57--66 (2015).
Toplam 8 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Araştırma Makalesi
Yazarlar

Said Melliani 0000-0002-5150-1185

Ahmed Chafiki Bu kişi benim

Lalla Saadia Chadli

Mohamed Oukessou Bu kişi benim

Yayımlanma Tarihi 31 Temmuz 2018
Gönderilme Tarihi 15 Mayıs 2018
Kabul Tarihi 5 Ağustos 2018
Yayımlandığı Sayı Yıl 2018 Cilt: 1 Sayı: 2

Kaynak Göster

APA Melliani, S., Chafiki, A., Chadli, L. S., Oukessou, M. (2018). NEW FRACTIONAL DERIVATIVE IN COLOMBEAU ALGEBRA. Journal of Universal Mathematics, 1(2), 180-189.
AMA Melliani S, Chafiki A, Chadli LS, Oukessou M. NEW FRACTIONAL DERIVATIVE IN COLOMBEAU ALGEBRA. JUM. Temmuz 2018;1(2):180-189.
Chicago Melliani, Said, Ahmed Chafiki, Lalla Saadia Chadli, ve Mohamed Oukessou. “NEW FRACTIONAL DERIVATIVE IN COLOMBEAU ALGEBRA”. Journal of Universal Mathematics 1, sy. 2 (Temmuz 2018): 180-89.
EndNote Melliani S, Chafiki A, Chadli LS, Oukessou M (01 Temmuz 2018) NEW FRACTIONAL DERIVATIVE IN COLOMBEAU ALGEBRA. Journal of Universal Mathematics 1 2 180–189.
IEEE S. Melliani, A. Chafiki, L. S. Chadli, ve M. Oukessou, “NEW FRACTIONAL DERIVATIVE IN COLOMBEAU ALGEBRA”, JUM, c. 1, sy. 2, ss. 180–189, 2018.
ISNAD Melliani, Said vd. “NEW FRACTIONAL DERIVATIVE IN COLOMBEAU ALGEBRA”. Journal of Universal Mathematics 1/2 (Temmuz 2018), 180-189.
JAMA Melliani S, Chafiki A, Chadli LS, Oukessou M. NEW FRACTIONAL DERIVATIVE IN COLOMBEAU ALGEBRA. JUM. 2018;1:180–189.
MLA Melliani, Said vd. “NEW FRACTIONAL DERIVATIVE IN COLOMBEAU ALGEBRA”. Journal of Universal Mathematics, c. 1, sy. 2, 2018, ss. 180-9.
Vancouver Melliani S, Chafiki A, Chadli LS, Oukessou M. NEW FRACTIONAL DERIVATIVE IN COLOMBEAU ALGEBRA. JUM. 2018;1(2):180-9.