Hyers–Ulam–Rassias Stability of Nonlinear Implicit Higher-Order Volterra Integrodifferential Equations from above on Unbounded Time Scales

Andrejs Reinfelds; Shraddha Christian

doi:10.3390/math12091379

Hyers–Ulam–Rassias Stability of Nonlinear Implicit Higher-Order Volterra Integrodifferential Equations from above on Unbounded Time Scales

Andrejs Reinfelds^*
, Shraddha Christian^*

^*Corresponding author for this work

Riga Technical University

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we present sufficient conditions for Hyers-Ulam-Rassias stability of nonlinear implicit higher-order Volterra-type integrodifferential equations from above on unbounded time scales. These new sufficient conditions result by reducing Volterra-type integrodifferential equations to Volterra-type integral equations, using the Banach fixed point theorem, and by applying an appropriate Bielecki type norm, the Lipschitz type functions, where Lipschitz coefficient is replaced by unbounded rd-continuous function.

Original language	English
Article number	1379
Pages (from-to)	1-10
Journal	Mathematics
Volume	12
Issue number	9
DOIs	https://doi.org/10.3390/math12091379
Publication status	Published - May 2024

Keywords

existence
Hyers–Ulam–Rassias stability
time scales
uniqueness
Volterra integrodifferential equations

OECD Field of Science

1.1 Mathematics

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10.3390/math12091379

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title = "Hyers–Ulam–Rassias Stability of Nonlinear Implicit Higher-Order Volterra Integrodifferential Equations from above on Unbounded Time Scales",

abstract = "In this paper, we present sufficient conditions for Hyers-Ulam-Rassias stability of nonlinear implicit higher-order Volterra-type integrodifferential equations from above on unbounded time scales. These new sufficient conditions result by reducing Volterra-type integrodifferential equations to Volterra-type integral equations, using the Banach fixed point theorem, and by applying an appropriate Bielecki type norm, the Lipschitz type functions, where Lipschitz coefficient is replaced by unbounded rd-continuous function.",

keywords = "existence, Hyers–Ulam–Rassias stability, time scales, uniqueness, Volterra integrodifferential equations",

author = "Andrejs Reinfelds and Shraddha Christian",

note = "Publisher Copyright: {\textcopyright} 2024 by the authors.",

year = "2024",

month = may,

doi = "10.3390/math12091379",

language = "English",

volume = "12",

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AU - Reinfelds, Andrejs

AU - Christian, Shraddha

PY - 2024/5

Y1 - 2024/5

N2 - In this paper, we present sufficient conditions for Hyers-Ulam-Rassias stability of nonlinear implicit higher-order Volterra-type integrodifferential equations from above on unbounded time scales. These new sufficient conditions result by reducing Volterra-type integrodifferential equations to Volterra-type integral equations, using the Banach fixed point theorem, and by applying an appropriate Bielecki type norm, the Lipschitz type functions, where Lipschitz coefficient is replaced by unbounded rd-continuous function.

AB - In this paper, we present sufficient conditions for Hyers-Ulam-Rassias stability of nonlinear implicit higher-order Volterra-type integrodifferential equations from above on unbounded time scales. These new sufficient conditions result by reducing Volterra-type integrodifferential equations to Volterra-type integral equations, using the Banach fixed point theorem, and by applying an appropriate Bielecki type norm, the Lipschitz type functions, where Lipschitz coefficient is replaced by unbounded rd-continuous function.

KW - existence

KW - Hyers–Ulam–Rassias stability

KW - time scales

KW - uniqueness

KW - Volterra integrodifferential equations

UR - https://www.mdpi.com/2227-7390/12/9/1379

UR - https://www.scopus.com/pages/publications/85192770884

U2 - 10.3390/math12091379

DO - 10.3390/math12091379

M3 - Article

SN - 2227-7390

VL - 12

SP - 1

EP - 10

JO - Mathematics

JF - Mathematics

IS - 9

M1 - 1379

ER -

Hyers–Ulam–Rassias Stability of Nonlinear Implicit Higher-Order Volterra Integrodifferential Equations from above on Unbounded Time Scales

Abstract

Keywords

OECD Field of Science

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