11 citations · 27 across the 12 of their papers we have counts for
12 papers
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…
On the stability of a hyperbolic fractional partial differential equation
J. Vanterler da C. Sousa, E. Capelas de OLiveira
In this paper, by means of the Gronwall inequality, the ψ-Riemann-Liouville fractional partial integral and the ψ-Hilfer fractional partial derivative are introduced and some of it…
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…
Ulam-Hyers-Rassias stability for a class of fractional integro-differential equations
J. Vanterler da C. Sousa, E. Capelas de Oliveira
By means of the recent -Hilfer fractional derivative and of the Banach fixed-point theorem, we investigate stabilities of Ulam-Hyers, Ulam-Hyers-Rassias and semi-Ulam-Hyers-Rass…