4 citations · 8 across the 5 of their papers we have counts for
8 papers · 1 filter
A new class of mild and strong solutions of integro-differential equation of arbitrary order in Banach space
J. Vanterler da C. Sousa, D. F. Gomes, E. Capelas de Oliveira
The motivation that the field of differential equations provide to several researchers for the challenges that have been challenging them over the decades has contributed to the st…
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…
On the fractional functional differential equation with abstract Volterra operator
J. Vanterler da C. Sousa, E. Capelas de Oliveira, Kishor D. Kucche
The present paper plans to examine the existence, uniqueness and data dependence of the solution of the fractional functional differential equation with the abstract operator of Vo…
Fractional order pseudoparabolic partial differential equation: Ulam-Hyers stability
J. Vanterler da C. Sousa, E. Capelas de Oliveira
Using Gronwall inequality we will investigate the Ulam-Hyers and generalized Ulam-Hyers-Rassias stabilities for the solution of a fractional order pseudoparabolic partial different…
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…