Evolution equations with fractional Gross Laplacian and Caputo time fractional derivative

Abstract

In this paper, we consider the evolution equations with fractional Gross Laplacian and generalized Caputo time fractional deravitive in infinite dimensional space of entire functions with growth condition. The convolution between a generalized function related to the Mittag–Leffler function and the initial condition has been given to demonstrate the explicit solutions. Moreover, we prove that the fundamental solution is related to the inverse stable subordinators and the symmetric $$\alpha $$ -stable distribution.