Ulam–Hyers–Rassias Stability for a Class of Fractional Integro-Differential Equations

By J. Vanterler, Danilo C. Sousa, E. Capelas de Oliveira. Results in Mathematics, 2018

143 citations recorded by the source corpus.

By means of the recent ψ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\psi $$\end{document}-Hilfer fractional derivative and of the Banach fixed-point theorem, we investigate stabilities of Ulam–Hyers, Ulam–Hyers–Rassias and semi-Ulam–Hyers–Rassias on closed intervals [a, b] and [a,∞)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$[a,\infty )$$\end{document} for a particular class of fractional integro-differential equations.

Subfields: Applied Mathematics, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/e84b8d5e6a5ad4dad80a845873160b231211847c

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In Applied Mathematics

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Citations in the corpus

Nonlocal boundary value problem for generalized Hilfer implicit fractional differential equations (2020, background): “The basic study about existence and uniqueness of the solution of a nonlinear φ-Hilfer FDEs with different kinds of initial conditions and the Ulam-Hyers and Ulam-Hyers-Rassias stabilities of its solutions have been explored in [22, 23, 24, 25, 26, 27, 28, 29] .”
The existence and Ulam–Hyers stability results for $$\psi $$-Hilfer fractional integrodifferential equations (2020, background): “Many authors investigated different types of stability of Hilfer FDEs, for instance, see [1,16,24,25,36].”
A Gronwall inequality and the Cauchy-type problem by means of ψ-Hilfer operator (2017, background): “In this sense, due to this exponential growth of the fractional calculus added to differential equations, the number of researchers involved in the investigation of existence, uniqueness, Ulam-Hyers stabilities of solutions of fractional differential equations of the type: impulsive, functional and ”
On the Nonlinear $\Psi$-Hilfer Hybrid Fractional Differential Equations (2020, background): “Investigation of initial and boundary value problems for Ψ-Hilfer about existence, uniqueness, data dependence and Ulam-Hyers stabilities may be found in [24, 25, 26, 27, 28, 29, 30, 31, 32, 33].”