Extends standard existence, stability, and dependence theorems to impulsive phi-Hilfer fractional differential equations, but the claimed result on dependence on the derivative order is not correctly proved.
A Gronwall inequality and the Cauchy-type problem by means of $\psi$-Hilfer operator
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
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 equation involving the $\psi$-Hilfer fractional derivative and the existence and uniqueness of solutions are discussed. Finally, through generalized Gronwall inequality, we prove the continuous dependence of data on the Cauchy-type problem.
fields
math.DS 1years
2019 1verdicts
REJECT 1representative citing papers
citing papers explorer
-
Analysis of Impulsive $\varphi$--Hilfer Fractional Differential Equations
Extends standard existence, stability, and dependence theorems to impulsive phi-Hilfer fractional differential equations, but the claimed result on dependence on the derivative order is not correctly proved.