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

A. O. Lopushansky, H. P. Lopushanska, O. V. Pasichnyk

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.

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