Results 71 to 80 of about 4,940 (143)

Interventions in Corruption Dynamics: A Computational Analysis With a Piecewise‐Modified Fractional‐Order Derivative

Discrete Dynamics in Nature and Society, Volume 2026, Issue 1, 2026.
Corruption behaves like a social contagion that evolves through interaction, influence, and institutional memory. To capture this complexity, we develop a deterministic corruption‐transmission model governed by a piecewise fractional framework that combines the Caputo and modified Atangana–Baleanu–Caputo (mABC) derivatives. This dual‐operator structure
Mati Ur Rahman, Refka Ghodhbani, Mehmet Yavuz, Saira Tabassum, Deepali   +4 more
wiley   +1 more source

Locally Bounded Second κ‐Variation Solution of an Integro‐Differential Equation With Infinite Delay

International Journal of Differential Equations, Volume 2026, Issue 1, 2026.
This work presents conditions under which the Volterra integral equation of the second kind admits a unique solution in the class of locally bounded second κ‐variation functions on [0, +∞). Our approach relies on successive Picard iterations to obtain such a solution on a compact interval, and then to prolong it to [0, +∞).
Luz Elimar Marchan, Luis Fernando Mejías, Liliana Pérez, Deepali   +3 more
wiley   +1 more source

Hyers–Ulam Stability of a System of Hyperbolic Partial Differential Equations

Mathematics, 2022
In this paper, we study Hyers–Ulam and generalized Hyers–Ulam–Rassias stability of a system of hyperbolic partial differential equations using Gronwall’s lemma and Perov’s theorem.
Daniela Marian, Sorina Anamaria Ciplea, Nicolaie Lungu   +2 more
doaj   +1 more source

On Hyers–Ulam–Rassias Stability of the Pexider Equation

Journal of Mathematical Analysis and Applications, 1999
Let \((G,+)\) be an abelian group, \((X,\|\cdot\|)\) be a Banach space and \(f,g,h:G\rightarrow X\) be mappings. An equation \(f(x+y)=g(x)+h(y)\) is called a Pexider functional equation. In the paper the stability of that equation in the spirit of Hyers-Ulam-Rassias is considered. The main theorem is the following: Let \(\varphi:G\times G\rightarrow[0,\
Jun, Kil-Woung, Shin, Dong-Soo, Kim, Byung-Do   +2 more
openaire   +2 more sources

Hyers–Ulam stability for a nonlinear iterative equation [PDF]

Colloquium Mathematicum, 2002
Hyers-Ulam stability of the nonlinear iterative functional equation \(G(f^{n_1}(x), \dots, f^{n_k}(x)) =F(x)\) is considered. \(F\) is assumed to be given and \(f\) an unknown function. Both \(F\) and \(f\) are self-maps of \(I\), a subset of a Banach space; \(G:I^k\to I\), where, as usual, \(I^k=I\times \cdots\times I\), \(f^0(x)=x\), \(f^{i+1}(x) =f ...
Xu, Bing, Zhang, Weinian
openaire   +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

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

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

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

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