On two new operators in fractional calculus and application

J. Vanterler da C. Sousa, E. Capelas de Oliveira

Published 2017-10-10Version 1

Motivated by the fractional derivative $\psi$-Riemann-Liouville and by the fractional derivative $\psi$-Hilfer, we introduced two new fractional operators: $\psi$-fractional integral and $\psi$-fractional derivative. We present and discuss relationships between these the two fractional operators, as well as, we guarantee that the $\psi$-fractional integration operator is limited. In this sense, we present some examples, in particular, that involve the Mittag-Leffler function, of paramount importance in the solution of population growth problem, as approached.