Non-convolutional general fractional operators and some of their properties

Abstract

In this work, we propose a general framework for fractional integrals without following a convolution-kernel approach, and consider the corresponding notions for fractional derivatives under different perspectives (Riemann–Liouville and Caputo-type), analyzing their main mathematical properties such as semi-group condition, and the linearity of the integral, as well as the first theorem of calculus. We study some connections between the different notions, and provide a generalized Sonin condition.