Results 51 to 60 of about 1,558 (136)

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

Optimal Control Analysis and Simulation of a Mathematical Model for Recurrent Malaria Dynamics via the Caputo Fractional‐Order Derivative

International Journal of Differential Equations, Volume 2026, Issue 1, 2026.
The Caputo fractional derivative is employed to investigate the role of memory effects in modeling the transmission dynamics of recurrent malaria in interacting human–vector populations. The model generalizes an existing classical version accounting for the three major forms of recurrent malaria, including re‐infection, recrudescence, and relapse.
Sulaimon F. Abimbade, Furaha M. Chuma, Adekunle O. Sangotola, Ramoshweu S. Lebelo, Samson Olaniyi, Md. Kamrujjaman   +5 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

An Implicit Fractional Model With Finite Delay and Impulses: Analysis and Computation

International Journal of Differential Equations, Volume 2026, Issue 1, 2026.
This paper establishes the existence and uniqueness of solutions for a class of implicit fractional Volterra–Fredholm integrodifferential equations with finite delay and instantaneous impulses. By employing the Banach contraction principle and Schaefer’s fixed‐point theorem, we provide a rigorous analytical foundation for our results.
Abdulrahman A. Sharif, Maha Hamood, Kirtiwant P. Ghadle, Patricia J. Y. Wong   +3 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

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

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

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

Ulam–Hyers stability for hybrid differential equations with mixed fractional derivatives and the μ-Laplacian operator

Open Mathematics
In this work, we investigate the Ulam–Hyers stability and generalized Ulam–Hyers stability for a class of hybrid differential equations involving both proportional fractional derivatives and classical derivatives, coupled with the μ-Laplacian operator ...
Maazouz Kadda, Ouardani Abderrahmane, Bechayeb Rabah, Moumen Abdelkader, Bouye Mohamed   +4 more
doaj   +1 more source

Ulam’s Type Stability of a Discrete Matrix Equation with Second-Order Difference and Single Delay

Mathematical and Computational Applications
In this paper, we investigate the Ulam stability problem for a second-order discrete matrix difference equation with a single delay. The primary aim of this work is to establish rigorous Ulam-type stability criteria for this class of delayed matrix ...
Maosong Yang, Guanli Xiao, Yumei Liao, Adan Ding   +3 more
doaj   +1 more source