Results 51 to 60 of about 1,498 (137)

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

Study on existence and stability analysis for implicit neutral fractional differential equations of ABC derivative

Partial Differential Equations in Applied Mathematics
In this paper, we study the existence, uniqueness, and stability analysis of non-linear implicit neutral fractional differential equations involving the Atangana–Baleanu derivative in the Caputo sense. The Banach contraction principle theorem is employed
V. Sowbakiya, R. Nirmalkumar, K. Loganathan, C. Selvamani   +3 more
doaj   +1 more source

Uniqueness and Ulam–Hyers–Rassias stability results for sequential fractional pantograph q-differential equations

Journal of Inequalities and Applications, 2022
We study sequential fractional pantograph q-differential equations. We establish the uniqueness of solutions via Banach’s contraction mapping principle.
Mohamed Houas, Francisco Martínez, Mohammad Esmael Samei, Mohammed K. A. Kaabar   +3 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

Deterministic and Fractional‐Order Modeling of Potato Disease Transmission Dynamics

International Journal of Differential Equations, Volume 2026, Issue 1, 2026.
Potato plant diseases are a significant concern because they reduce crop yields and quality, putting the global food supply at risk. Our goal in developing this deterministic, fractional‐order epidemic model is to explain the transmission of these diseases by simulating the interactions between susceptible, exposed, infected, treated, and recovered ...
Md. Asraful Islam, Sherajum Arafin Kona, Kartik Ariyur   +2 more
wiley   +1 more source

Stability of generalized Newton difference equations

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2012
In the paper we discuss a stability in the sense of the generalized Hyers-Ulam-Rassias for functional equations Δn(p, c)φ(x) = h(x), which is called generalized Newton difference equations, and give a sufficient condition of the generalized Hyers-Ulam ...
Wang Zhihua, Shi Yong-Guo
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

Memory‐Dependent Chaotic Dynamics and Stabilization of a Nonlinear Fractional‐Order Financial System With Optimal Control

Journal of Applied Mathematics, Volume 2026, Issue 1, 2026.
This study presents an innovative nonlinear fractional‐order financial model that employs Caputo and Caputo–Fabrizio fractional derivatives to represent the dynamic interactions among interest rates, investment demand, price indices, and income/output. The model is formulated as a system of coupled nonlinear differential equations to encapsulate memory‐
Md. Asraful Islam, Razia Sultana, Payer Ahmed, Huaiqin Wu   +3 more
wiley   +1 more source

Existence and Uniqueness of Solutions to Initial Value Problems of High‐Order Fractional Fuzzy Differential Equations

Journal of Applied Mathematics, Volume 2026, Issue 1, 2026.
High‐order fractional fuzzy differential equations show great potential in modeling complex systems with memory effects and uncertainty. Existing qualitative theories seldom involve both Caputo‐type strongly generalized Hukuhara differentiability and coupled integral operators on infinite intervals. This paper presents a systematic investigation of the
Yanli Xi, Wenbin Bao, Mohammad Rezwan Habib   +2 more
wiley   +1 more source

Ulam-Hyers Stability and Ulam-Hyers-Rassias Stability for Fuzzy Integrodifferential Equation

Complexity, 2019
In this paper, we establish the Ulam-Hyers stability and Ulam-Hyers-Rassias stability for fuzzy integrodifferential equations by using the fixed point method and the successive approximation method.
Nguyen Ngoc Phung, Bao Quoc Ta, Ho Vu
doaj   +1 more source