This paper discusses and provides some analytical studies for a modified fractional-order SIRD mathematical model of the COVID-19 epidemic in the sense of the Caputo–Katugampola fractional derivative that allows treating of the biological models of infectious diseases and unifies the Hadamard and Caputo fractional derivatives into a single form. By considering the vaccine parameter of the suspected population, we compute and derive several stability results based on some symmetrical parameters that satisfy some conditions that prevent the pandemic. The paper also investigates the problem of the existence and uniqueness of solutions for the modified SIRD model. It does so by applying the properties of Schauder’s and Banach’s fixed point theorems.

Predicting the next event (or symbol) of a sequence has many applications such as network event prediction, webpage prefetching, activity recommendation and stock price prediction. An effective approach for event prediction that has the benefit of being interpretable, is to extract episode rules to then apply them for prediction. This paper improves upon this approach by using a novel type of episode rules called partially-ordered episode rules. These rules are more general than standard episode rules as they loosen the ordering constraint on events in each rule antecedent and consequent. Hence, a partially-ordered episode rule can replace multiple standard episode rules. Experiments on several benchmark datasets show that partially-ordered episode rules can provide more accurate predictions than standard episode rules.

This paper investigates the problem of the existence and uniqueness of solutions under the generalized self-similar forms to the space-fractional diffusion equation. Therefore, through applying the properties of Schauder’s and Banach’s fixed point theorems; we establish several results on the global existence and blow-up of generalized self-similar solutions to this equation.