12 citations · 18 across the 6 of their papers we have counts for
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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…
On the Ulam-Hyers-Rassias stability for nonlinear fractional differential equations using the -Hilfer operator
J. Vanterler da C. Sousa, E. Capelas de Oliveira
We study the existence and uniqueness of solution of a nonlinear Cauchy problem involving the -Hilfer fractional derivative. In addition, we discuss the Ulam-Hyers and Ulam-Hyer…
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…