12 citations · 16 across the 7 of their papers we have counts for
7 papers
Mild and strong solutions for Hilfer evolution equation
J. Vanterler da C. Sousa, Leandro S. Tavares, E. Capelas de Oliveira
In this paper, we investigate the existence and uniqueness of mild and strong solutions of fractional semilinear evolution equations in the Hilfer sense, by means of Banach fixed p…
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…