On some properties of generalized cardinal sine kernel fractional operators: Advantages and applications of the extended operators

Abstract

A new Caputo-type fractional derivative model with a generalized cardinal sine kernel and its singular kernel extension were presented. In this paper, we used the Laplace transform as an effective tool to study the considered fractional derivative models. Then, we introduced the Riemann–Liouville-type for the studied generalized cardinal sine fractional derivative model. Next, a general framework of the generalized cardinal sine kernel fractional derivative model and its singular kernel extension in relation to functions is presented. Some properties of the studied fractional derivative operators and relationships such as the relation between fractional integral and derivative operators are discussed. The dynamics of some nonlinear fractional order models are simulated, using a numerical algorithm formulated in this paper, to demonstrate the motivations of using the extended operators. The extended version of the considered fractional derivative operators provided useful suggestions regarding the modeling issue.