4 citations · 12 across the 8 of their papers we have counts for
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Leibniz type rule: Hilfer fractional derivative
J. Vanterler da C. Sousa, E. Capelas de Oliveira
In this paper, we present the Leibniz rule for the Hilfer (H) fractional derivative in two versions, the first in relation to RL fractional derivative and the second in…
A new fractional derivative of variable order with non-singular kernel and fractional differential equations
J. Vanterler da C. Sousa, E. Capelas de Oliveira
In this paper, we introduce two new non-singular kernel fractional derivatives and present a class of other fractional derivatives derived from the new formulations. We present som…
A note on the Laplace transform and the variable-order differential operators
J. Vanterler da C. Sousa, E. Capelas de Oliveira
In this short note, using the variable-order differential operator introduced by means of the inverse Laplace transform \cite{coimbra}, we questioned the result obtained by Yang an…
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 truncated -fractional derivative in
J. Vanterler da C. Sousa, E. Capelas de Oliveira
Using the six parameters truncated Mittag-Leffler function, we introduce a convenient truncated function to define the so-called truncated -fractional derivative type.…
Gruss-type inequality by mean of a fractional integral
J. Vanterler da C. Sousa, D. S. Oliveira, E. Capelas de Oliveira
In this paper, using a fractional integral as proposed by Katugampola we establish a generalization of integral inequalities of Gruss-type. We prove two theorems associated with th…