Results 51 to 60 of about 6,522 (226)

Ulam‐type stability of ψ− Hilfer fractional‐order integro‐differential equations with multiple variable delays

Asian Journal of Control, Volume 28, Issue 1, Page 34-45, January 2026.
Abstract We study a nonlinear ψ−$$ \psi - $$ Hilfer fractional‐order delay integro‐differential equation ( ψ−$$ \psi - $$ Hilfer FrODIDE) that incorporates N−$$ N- $$ multiple variable time delays. Utilizing the ψ−$$ \psi - $$ Hilfer fractional derivative ( ψ−$$ \psi - $$ Hilfer‐FrD), we investigate the Ulam–Hyers––Rassias (U–H–R), semi‐Ulam–Hyers ...
Cemil Tunç, Osman Tunç
wiley   +1 more source

The Hyers–Ulam stability of nonlinear recurrences

Journal of Mathematical Analysis and Applications, 2007
In the paper of \textit{D. Popa} [J. Math. Anal. Appl. 309, No. 2, 591--597 (2005; Zbl 1079.39027)] the Hyers-Ulam stability problem was proved for linear recurrences in a Banach space. In the paper under review, the authors investigate this problem for nonlinear recurrences in a metric space \((X, d)\). More precisely, they show that if \(\{x_n\}\), \(
Brzdȩk, Janusz, Popa, Dorian, Xu, Bing
openaire   +1 more source

Hyers-Ulam and Hyers-Ulam-Rassias Stability for a Class of Integro-Differential Equations [PDF]

, 2018
We analyse different kinds of stabilities for a class of very general nonlinear integro-differential equations of Volterra type within appropriate metric spaces. Sufficient conditions are obtained in view to guarantee Hyers-Ulam stability and Hyers-Ulam-Rassias stability for such a class of integro-differential equations. We will consider the different
Castro, L. P., Simões, A. M.
openaire   +4 more sources

Study of a nonlinear multi-terms boundary value problem of fractional pantograph differential equations

Advances in Difference Equations, 2021
In this research work, a class of multi-term fractional pantograph differential equations (FODEs) subject to antiperiodic boundary conditions (APBCs) is considered.
Muhammad Bahar Ali Khan, Thabet Abdeljawad, Kamal Shah, Gohar Ali, Hasib Khan, Aziz Khan   +5 more
doaj   +1 more source

Continuous Dependence on the Initial Functions and Stability Properties in Hyers–Ulam–Rassias Sense for Neutral Fractional Systems with Distributed Delays

Fractal and Fractional, 2023
We study several stability properties on a finite or infinite interval of inhomogeneous linear neutral fractional systems with distributed delays and Caputo-type derivatives.
Hristo Kiskinov, Mariyan Milev, Magdalena Veselinova, Andrey Zahariev   +3 more
doaj   +1 more source

On the Orthogonal Stability of the Pexiderized Quadratic Equation

, 2005
The Hyers--Ulam stability of the conditional quadratic functional equation of Pexider type f(x+y)+f(x-y)=2g(x)+2h(y), x\perp y is established where \perp is a symmetric orthogonality in the sense of Ratz and f is odd.Comment: 10 pages, Latex; Changed ...
Aczél J., Aczél J., Czerwik S., Czerwik S., Drljević F., Ger R., Hyers D.H., Jun K.W., Jung S.M., Mohammad Sal Moslehian, Moslehian M.S., Rassias Th.M., Vajzović F.   +12 more
core   +2 more sources

Fixed Point Analysis for Cauchy‐Type Variable‐Order Fractional Differential Equations With Finite Delay

International Journal of Differential Equations, Volume 2026, Issue 1, 2026.
This paper presents a comprehensive analysis of the existence, uniqueness, and Ulam–Hyers stability of solutions for a class of Cauchy‐type nonlinear fractional differential equations with variable order and finite delay. The motivation for this study lies in the increasing importance of variable‐order fractional calculus in modeling real‐world systems
Souhila Sabit, Mohammed Said Souid, Marwa Benaouda, K. Sudarmozhi, Joshua Kiddy K. Asamoah, Amar Nath Chatterjee   +5 more
wiley   +1 more source

Generalized Hyers-Ulam Stability of Trigonometric Functional Equations [PDF]

Mathematics, 2018
In the present paper we study the generalized Hyers–Ulam stability of the generalized trigonometric functional equations f ( x y ) + μ ( y ) f ( x σ ( y ) ) = 2 f ( x ) g ( y ) + 2 h ( y ) , x , y ∈ S ; f ( x y ) + μ ( y ) f ( x σ ( y ) ) = 2 f ( y ) g ( x ) + 2 h ( x ) , x , y ∈ S , where S is a semigroup, σ : S ⟶ S is a ...
Elqorachi, Elhoucien, Rassias, Michael Th.   +1 more
openaire   +2 more sources

Stability of Partial Differential Equations by Mahgoub Transform Method

Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 2022
The stability theory is an important research area in the qualitative analysis of partial differential equations. The Hyers-Ulam stability for a partial differential equation has a very close exact solution to the approximate solution of the differential
Harun Biçer
doaj   +1 more source

Neuronal Dynamics of an Intrinsically Bursting Neuron Through the Caputo–Fabrizio Fractal–Fractional Hodgkin–Huxley Model

International Journal of Differential Equations, Volume 2026, Issue 1, 2026.
This study introduces a novel fractal–fractional extension of the Hodgkin–Huxley model to capture complex neuronal dynamics, with particular focus on intrinsically bursting patterns. The key innovation lies in the simultaneous incorporation of Caputo–Fabrizio operators with fractional order α for memory effects and fractal dimension τ for temporal ...
M. J. Islam, M. J. Abedin, A. Hoque, M. G. Hafez, Jaume Giné   +4 more
wiley   +1 more source