Document Type: Research Paper

**Authors**

Department of Mathematics, University of Mazandaran, Babolsar, Iran.

**Abstract**

This work concerns the study of existence and uniqueness to heat equation with fractional Laplacian dierentiation in extended Colombeau algebra.

**Keywords**

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

[5] S. G. Samko ,

*On spaces of Riesz potentials*, Math. USSR lzvestija, 1976.

[6] M. Stojanovic},

*Extension of Colombeau algebra to derivatives of arbitrary*

*order D*

^{α}, αεR_{+}U{0}. Application to ODEs and*PDEs with entire and fractional derivatives*, Nonlinear Analysis 5 (2009) 5458-5475.