Abstract
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.
Highlights
There has been a considerable interest in studying Ulam type stability, as soon as it was formulated in 1940 [39]
The same authors in [22] were motivated by the results obtained by Rus [33], Otrocol [27], and Otrocol et al [28] to discuss the existence and uniqueness of solutions and Ulam stability for nonlinear Volterra delay integro-differential equations t x (t) = f t, x(t), x g(t), h t, s, x(s), x g(s) ds, t ∈ I = [0, b], b > 0, where f ∈ C(I × R3 × R), h ∈ C(I × I × R2 × R), g ∈ C(I, [–r, b]), 0 < r < ∞, and g(t) ≤ t
Flhi [12] established some fixed point results for α – λ-contractions in the class of quasi b-metric spaces, where he provided some examples and an application on a solution of an integral equation
Summary
There has been a considerable interest in studying Ulam type stability, as soon as it was formulated in 1940 [39]. Alsulami [6] defined a class of general type α-admissible contraction mappings on quasi-b-metric-like spaces They discussed the existence and uniqueness of fixed points for this class of mappings and the results applied to Ulam stability problems. Flhi [12] established some fixed point results for α – λ-contractions in the class of quasi b-metric spaces, where he provided some examples and an application on a solution of an integral equation He studied the stability of Ulam–Hyers and well-posedness of a fixed point problem. In 2019, Alqahtani et al [4] proposed a solution for Volterra type fractional integral equations by using a hybrid type contraction that unifies both nonlinear and linear type inequalities in the context of metric spaces Besides this main goal, the authors merged several existing fixed point theorems that were formulated by linear and nonlinear contractions. At the end of the paper, we give some illustrative applications
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
