4 citations · 12 across the 6 of their papers we have counts for
6 papers
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…
The Minkowski's inequality by means of a generalized fractional integral
J. Vanterler da C. Sousa, E. Capelas de Oliveira
We use the definition of a fractional integral, recently proposed by Katugampola, to establish a generalization of the reverse Minkowski's inequality. We show two new theorems asso…