arXiv Analytics

Sign in

arXiv:1709.03634 [math.CA]AbstractReferencesReviewsResources

A Gronwall inequality and the Cauchy-type problem by means of $ψ$-Hilfer operator

J. Vanterler da Costa Sousa, E. Capelas de Oliveira

Published 2017-09-12Version 1

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.

Comments: 19 pages
Categories: math.CA
Subjects: 26A33, 36A08, 34A12, 34A40
Related articles: Most relevant | Search more
arXiv:1704.02174 [math.CA] (Published 2017-04-07)
Existence and uniqueness of solution of Cauchy-type problem for Hilfer fractional differential equations
arXiv:1507.05567 [math.CA] (Published 2015-07-20)
On quasi-periodicity properties of fractional integrals and fractional derivatives of periodic functions
arXiv:1212.1423 [math.CA] (Published 2012-12-06)
Application of multidimensional Hardy operator and its connection with a certain nonlinear differential equation in weighted variable Lebesgue spaces

Links

Toolbox