| Resumo: | Two mathematical tendencies are targeted in this doctoral thesis, the first is related to the establishment of certain theoretical results within the theory of the calculus of variations, on one hand, a stochastic fractional integration by parts formula and a stochastic fractional Euler-Lagrange equation are obtained, on the other hand, weighted generalized fractional Taylor's theorem and Euler Lagrange equation with non-singular kernel sense are studied. The second trend was aimed at enriching the literature with several mathematical applications in different fields, with the idea of providing various appropriate solutions to complex social problems, namely those constructed with the outbreak of the COVID-19 pandemic, in addition, the description of some adequate solutions in both bio-mathematics and bio-economics.
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