Hyers–Ulam stability of impulsive Volterra delay integro-differential equations

This paper discusses different types of Ulam stability of first-order nonlinear Volterra delay integro-differential equations with impulses. Such types of equations allow the presence of two kinds of memory effects represented by the delay and the kernel of the used fractional integral operator. Our...

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Bibliographic Details
Published in:Advances in difference equations Vol. 2021; no. 1; pp. 1 - 13
Main Authors: Refaai, D. A., El-Sheikh, M. M. A., Ismail, Gamal A. F., Abdalla, Bahaaeldin, Abdeljawad, Thabet
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 30.10.2021
Springer Nature B.V
SpringerOpen
Subjects:
Analysis
Delay
Delay integro-differential equation
Difference and Functional Equations
Differential equations
Fixed Point Theory and Applications to Fractional Ordinary and Partial Difference and Differential Equations
Fractional calculus
Functional Analysis
Impulses
Inequality
Integral equations
Mathematical analysis
Mathematics
Mathematics and Statistics
Operators (mathematics)
Ordinary Differential Equations
Partial Differential Equations
Stability
Ulam–Hyers stability
Delay integro-differential equation
Impulses
Ulam–Hyers stability
ISSN:1687-1847, 1687-1839, 1687-1847
Online Access:Get full text
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Summary:This paper discusses different types of Ulam stability of first-order nonlinear Volterra delay integro-differential equations with impulses. Such types of equations allow the presence of two kinds of memory effects represented by the delay and the kernel of the used fractional integral operator. Our analysis is based on Pachpatte’s inequality and the fixed point approach represented by the Picard operators. Applications are provided to illustrate the stability results obtained in the case of a finite interval.
Bibliography:ObjectType-Article-1
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content type line 14
ISSN:1687-1847
1687-1839
1687-1847
DOI:10.1186/s13662-021-03632-1