Department of Mathematics, University of Mazandaran, Babolsar, Iran


In this paper, we establish the existence and uniqueness result of the linear Schrodinger equation with Marchaud fractional derivative in Colombeau generalized algebra. The purpose of introducing Marchaud fractional derivative is regularizing it in Colombeau sense.


Main Subjects

[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.