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

الموضوعات :

M. Alimohammady ¹ , F. Fattahi ²

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

تاريخ الإرسال : 23 السبت , شعبان, 1435 تاريخ التأكيد : 11 الخميس , ذو الحجة, 1436 تاريخ الإصدار : 07 الأربعاء , ذو الحجة, 1435

الکلمات المفتاحية: Colombeau algebra, Marchaud fractional differentiation, Schrodinger equation,

ملخص المقالة :

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

المصادر:

[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.