12 citations · 21 across the 9 of their papers we have counts for
6 papers · 1 filter
Ulam-Hyers stability of a nonlinear fractional Volterra integro-differential equation
J. Vanterler da C. Sousa, E. Capelas de Oliveira
Using the Hilfer fractional derivative, we present a study of the Hyers-Ulam-Rassias stability and the Hyers-Ulam stability of the fractional Volterra integral-differential equ…
A Gronwall inequality and the Cauchy-type problem by means of -Hilfer operator
J. Vanterler da Costa Sousa, E. Capelas de Oliveira
In this paper, we propose a generalized Gronwall inequality through the fractional integral with respect to another function. The Cauchy-type problem for a nonlinear differential e…
On the -Hilfer fractional derivative
J. Vanterler da C. Sousa, E. Capelas de Oliveira
In this paper we introduce a new fractional derivative with respect to another function the so-called -Hilfer fractional derivative. We discuss some properties and important res…
Analytic components for the hadronic total cross-section: Fractional calculus and Mellin transform
E. Capelas de Oliveira, M. J. Menon, P. V. R. G. Silva
In high-energy hadron-hadron collisions, the dependence of the total cross-section () with the energy still constitutes an open problem for QCD. Phenomenological analyses…
Truncated -fractional Taylor's formula with applications
J. Vanterler da C. Sousa, E. Capelas de Oliveira
In this paper, we present and prove a new truncated -fractional Taylor's formula using the truncated -fractional variation of constants formula. In this s…
Mittag-Leffler functions and the truncated -fractional derivative
J. Vanterler da C. Sousa, E. Capelas de Oliveira
We introduce a new derivative, the so-called truncated -fractional derivative for -differentiable functions through the six parameters truncated Mittag-Leffler func…