Bridging the gap between models based on ordinary, delayed, and fractional differentials equations through integral kernels.

ABSTRACT: Evolution equations with convolution-type integral operators have a history of study, yet a gap exists in the literature regarding the link between certain convolution kernels and new models, including delayed and fractional differential equations. We demonstrate, starting from the logistic model structure, that classical, delayed, and fractional models are special cases of a framework using a gamma Mittag-Leffler memory kernel. We discuss and classify different types of this general kernel, analyze the asymptotic behavior of the general model, and provide numerical simulations. A detailed classification of the memory kernels is presented through parameter analysis. The fractional models we constructed possess distinctive features as they maintain dimensional balance and explicitly relate

SUBMITTER: Zeraick Monteiro N 

PROVIDER: S-EPMC11087811 | biostudies-literature | 2024 May

REPOSITORIES: biostudies-literature