Results 71 to 80 of about 5,043 (195)

On Generalized Hyers‐Ulam Stability of Admissible Functions [PDF]

Abstract and Applied Analysis, 2012
We consider the Hyers‐Ulam stability for the following fractional differential equations in sense of Srivastava‐Owa fractional operators (derivative and integral) defined in the unit disk: , in a complex Banach space. Furthermore, a generalization of the admissible functions in complex Banach spaces is imposed, and applications are illustrated.
openaire   +3 more sources

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

The Approximation Property of a One-Dimensional, Time Independent Schrödinger Equation with a Hyperbolic Potential Well

Mathematics, 2020
A type of Hyers–Ulam stability of the one-dimensional, time independent Schrödinger equation was recently investigated; the relevant system had a parabolic potential wall.
Ginkyu Choi, Soon-Mo Jung
doaj   +1 more source

Existence and Uniqueness of Nonlinear Volterra Integral Equations With Variable Fractional Order in Fréchet Spaces via a Frigon−Granas Fixed Point Approach

International Journal of Differential Equations, Volume 2026, Issue 1, 2026.
This paper investigates the existence and uniqueness of solutions to nonlinear Volterra integral equations of variable fractional order in Fréchet spaces. The variable‐order fractional derivative is considered in the Riemann–Liouville sense, which extends classical approaches and is central to the paper’s novelty.
Mohamed Telli, Benoumran Telli, Mohammed Said Souid, K. Sudarmozhi, Joshua Kiddy K. Asamoah, Khalil Ezzinbi   +5 more
wiley   +1 more source

Mittag-Leffler-Hyers-Ulam stability for a first- and second-order nonlinear differential equations using Fourier transform

Demonstratio Mathematica
In this article, we apply the Fourier transform to prove the Hyers-Ulam and Hyers-Ulam-Rassias stability for the first- and second-order nonlinear differential equations with initial conditions.
Selvam Arunachalam, Sabarinathan Sriramulu, Selvan Arumugam Ponmana   +2 more
doaj   +1 more source

Study on Approximate C∗‐Bimultiplier and JC∗‐Bimultiplier in C∗‐Ternary Algebra

International Journal of Mathematics and Mathematical Sciences, Volume 2026, Issue 1, 2026.
An additive‐quadratic mapping F:A×A⟶B is one that adheres to the following equations: Fr+s,t=Fr,t+Fs,t,Fr,s+t+Fr,s−t=22Fr,s+Fr,t. This paper leverages the fixed‐point method to investigate C∗‐bimultiplier and JC∗‐bimultiplier approximations on C∗‐ternary algebras. The focus is on the additive‐quadratic functional equation: Fr+s,t+u+Fr+s,t−u=2222Fr,t+Fr,
Mina Mohammadi, Javad Shokri, Saeid Ostadbashi, Abdul Rauf Khan   +3 more
wiley   +1 more source

Nonlinear analysis for Hilfer fractional differential equations

Franklin Open
In this paper, we discuss nonlinear Hilfer fractional differential equations with separated boundary conditions. Using the well-known Leggett–Williams theorem, we first explore the existence of multiple positive solutions for the nonlinear Hilfer ...
Debananda Basua, Swaroop Nandan Bora
doaj   +1 more source

Stability and Superstability of a Linear Functional Equation on Restricted Domains

Journal of Function Spaces, Volume 2026, Issue 1, 2026.
This paper investigates the Hyers–Ulam stability and superstability of the functional equation f(x2 + yf(z)) = xf(x) + zf(y) for real‐valued functions f : R⟶R on some restricted subsets of R.
Abbas Najati, Mohammad Amin Tareeghee, Themistocles M. Rassias, Arnab Biswas   +3 more
wiley   +1 more source

On the Stability of Fractional Integro‐Differential Equations of Ψ‐Hilfer Type

Journal of Function Spaces, Volume 2026, Issue 1, 2026.
In this article, we investigate some properties such as the existence, uniqueness, and Ulam–Hyers–Rassias stability for the fractional Volterra–Fredholm integrodifferential equations of Ψ‐Hilfer type with boundary conditions. We prove the desired results by using the Banach fixed point theorem and the Schauder fixed point theorem.
Malayin A. Mohammed, Sahar M. A. Maqbol, Ram G. Metkar, Udhayakumar Ramalingam   +3 more
wiley   +1 more source

Stability analysis of implicit fractional differential equations with anti-periodic integral boundary value problem

Annales Universitatis Paedagogicae Cracoviensis: Studia Mathematica, 2019
In this manuscript, we study the existence, uniqueness and various kinds of Ulam stability including Ulam-Hyers stability, generalized Ulam-Hyers stability, Ulam-Hyers-Rassias stability, and generalized Ulam-Hyers-Rassias stability of the solution to an ...
Akbar Zada, Hira Waheed
doaj