Czechoslovak Mathematical Journal, Vol. 67, No. 1, pp. 123-141, 2017
Pseudo almost periodicity of fractional integro-differential equations with impulsive effects in Banach spaces
Received July 22, 2015. First published February 24, 2017.
Abstract: In this paper, for the impulsive fractional integro-differential equations involving Caputo fractional derivative in Banach space, we investigate the existence and uniqueness of a pseudo almost periodic $PC$-mild solution. The working tools are based on the fixed point theorems, the fractional powers of operators and fractional calculus. Some known results are improved and generalized. Finally, existence and uniqueness of a pseudo almost periodic $PC$-mild solution of a two-dimensional impulsive fractional predator-prey system with diffusion are investigated.
Keywords: impulsive fractional integro-differential equation; pseudo almost periodicity; probability density; fractional powers of operator