# Two definitions of the generalized Cauchy problem for semi-linear diffusion equation with fractional derivative with respect to time

## Keywords:

semi-linear equation, generalized function, weight functional space, convolution, fractional derivative
Published online:
2012-06-28

### Abstract

Different equivalent definitions of the Cauchy problem for semi-linear diffusion equation with fractional derivative with respect to time and with the generalized function in the initial condition are offered. The existence and uniqueness theorem and the representation of the solution of such problem for linear homogeneous diffusion equation with fractional derivative with respect to time are obtained.

How to Cite

(1)

Lopushansky, A.; Lopushanska, H.; Pasichnyk, O. Two Definitions of the Generalized Cauchy Problem for Semi-Linear Diffusion Equation With Fractional Derivative With Respect to Time.

*Carpathian Math. Publ.***2012**,*4*, 72-82.