NEW FRACTIONAL DERIVATIVE IN COLOMBEAU ALGEBRA

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]).

Anahtar Kelimeler

• Colombeau algebra,Generalized functions

Kaynakça

1. J. F. Colombeau, Elementary Introduction in New Generalized Functions, North Holland, Amsterdam, 1985.
2. M. Stojanovic, Fondation of the fractional calculus in generalized function algebras, Analysis And Applications, Vol. 10 No. 4, 439--467 (2012).
3. M. Oberguggenberger, Generalized functions in nonlinear models a survey, Nonlinear Analysis 47, 5040--5049 (2001).
4. 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)
5. 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).
6. D. Rajter-Ciric, A note on fractional derivatives of Colombeau generalized stochastic processes, Novi Sad J. Math. 40, No 1, 111--121 (2010).
7. R. Khalil, M. Al Horani, A. Yousef, And M. Sababheh, A new definition of fractional derivative, J. Comput. Appl. Math. 264, 65--70 (2014).
8. T. Abdeljawad, On conformable fractional calculus, J. Comput. Appl. Math. Vol. 279 (C), 57--66 (2015).