Existence and uniqueness of solution of Schrodinger equation in extended Colombeau algebra

Subject Areas : Difference and functional equations

M. Alimohammady ¹ , F. Fattahi ²

1 - Department of Mathematics, University of Mazandaran, Babolsar, Iran
2 - Department of Mathematics, University of Mazandaran, Babolsar, Iran

Received: 2014-06-21 Accepted : 2015-09-24 Published : 2014-10-01

Keywords:

References:

[1] J. F. Colombeau, New generalized functions and Multiplication of distributions, North-Holland, Amsterdam, 1984.

 

[2] J. F. Colombeau and A. Y. L. Roux, Multiplications of distributions in elasticity and hydrodynamics, J. Math. Phys., 29 (1988), 315-319.

 

[3] J. F. Colombeau, Elementary Introduction to New Generalized Functions, North-Holland Math. Studies Vol. 113, North-Holland, Amsterdam 1985.

 

[4] I. M. Gel'fand and G. E. Shilov, Generalized functions, Academic press, New York, Vol. I, 1964.

 

[5] D. Rajter-Ciric, Fractional derivatives of Colombeau Generalized stochastic processes defined on R+, Appl. Anal. Discrete Math. 5 (2011), 283-297.

 

[6] M. Stojanovic , Extension of Colombeau algebra to derivatives of arbitrary order $D^{\alpha}$, Application to ODEs and PDEs with entire and fractional derivatives, Nonlinear Analysis 5 (2009), 5458-5475.