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NEW FRACTIONAL DERIVATIVE IN COLOMBEAU ALGEBRA

Year 2018, Volume: 1 Issue: 2, 180 - 189, 31.07.2018

Abstract

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]).

References

  • 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).
Year 2018, Volume: 1 Issue: 2, 180 - 189, 31.07.2018

Abstract

References

  • 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).
There are 8 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Said Melliani 0000-0002-5150-1185

Ahmed Chafiki This is me

Lalla Saadia Chadli

Mohamed Oukessou This is me

Publication Date July 31, 2018
Submission Date May 15, 2018
Acceptance Date August 5, 2018
Published in Issue Year 2018 Volume: 1 Issue: 2

Cite

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. July 2018;1(2):180-189.
Chicago Melliani, Said, Ahmed Chafiki, Lalla Saadia Chadli, and Mohamed Oukessou. “NEW FRACTIONAL DERIVATIVE IN COLOMBEAU ALGEBRA”. Journal of Universal Mathematics 1, no. 2 (July 2018): 180-89.
EndNote Melliani S, Chafiki A, Chadli LS, Oukessou M (July 1, 2018) NEW FRACTIONAL DERIVATIVE IN COLOMBEAU ALGEBRA. Journal of Universal Mathematics 1 2 180–189.
IEEE S. Melliani, A. Chafiki, L. S. Chadli, and M. Oukessou, “NEW FRACTIONAL DERIVATIVE IN COLOMBEAU ALGEBRA”, JUM, vol. 1, no. 2, pp. 180–189, 2018.
ISNAD Melliani, Said et al. “NEW FRACTIONAL DERIVATIVE IN COLOMBEAU ALGEBRA”. Journal of Universal Mathematics 1/2 (July 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 et al. “NEW FRACTIONAL DERIVATIVE IN COLOMBEAU ALGEBRA”. Journal of Universal Mathematics, vol. 1, no. 2, 2018, pp. 180-9.
Vancouver Melliani S, Chafiki A, Chadli LS, Oukessou M. NEW FRACTIONAL DERIVATIVE IN COLOMBEAU ALGEBRA. JUM. 2018;1(2):180-9.