Journal of Fractional Calculus and Nonlinear Systems

Hyers-Ulam Stability Results for Tempered (k, ψ)-Hilfer Fractional Differential Equations via the (k, ψ)-Generalized Laplace Transform

2026-01-16T11:40:28+00:00

We study the Hyers-Ulam stability of tempered (k, ψ)-Hilfer fractional differential equations using the (k, ψ)-generalized Laplace transform. This transform plays a central role in deriving and extending stability results, underscoring its effectiveness in the analysis of tempered fractional operators. The theoretical contributions are further supported by illustrative examples that confirm the validity and applicability of the results.

Analysis of Stability in Rulkov Neural Networks with Fractional Orders and Asymmetric Memristor Synapses

2025-11-24T12:54:39+00:00

Fractional-order models effectively capture memory and hereditary effects in neural and nonlinear dy namical systems. Memristors are ideal components for modeling synaptic connections due to their ability to emulate plasticity and memory effects. Discrete models of memristor-coupled neurons simplify computa tions and enable efficient analysis of large-scale networks. Despite their potential, discrete fractional-order memristor-coupled models have been less explored. To address this, we propose two novel discrete fractional order neural systems. The first system is a two-neuron motif coupled via dual memristors, while the second extends this configuration to a ring-shaped network of similar subnetworks. A new theorem on the stabil ity of discrete fractional-order systems is established, defining stability regions for both models. Numerical simulations illustrate the theoretical results and investigate how the fractional order, asymmetric memristive coupling, and other model and network parameters jointly influence the dynamics and stability of discrete time neurons.

Lie symmetry analysis of time fractional Burgers equation with time-dependent coefficients

2025-07-18T10:10:56+00:00

In this paper, Lie symmetry analysis is applied to study time fractional Burgers equation with time dependent coefficients. Some Lie symmetries for the equation with some kinds of coefficients f(t) and g(t) are obtained. They are used to reduce the aimed equation with Riemann-Liouville fractional derivative to the fractional ordinary equation with Erdélyi-Kober fractional derivative. Then the power series method is applied to derive explicit power series solution for the reduced equation. For the power series solution, we not only provide a proof of its convergence but also conduct numerical simulations and analysis. In addition, the new conservation theorem and the generalization of Noether operators are developed to construct the conservation laws for the equation studied.

NUMERICAL SIMULATIONS AND CONTROL STRATEGIES FOR COVID-19 AND MONKEYPOX CO-INFECTION DYNAMICS

2026-04-25T20:31:50+00:00

This study is a continuation of [16], which developed a deterministic model for the co-infection dynam ics of COVID-19 and Monkeypox, including model formulation, basic properties, reproduction numbers, and stability analyses of both disease-free and endemic equilibria. In this extension, we further investigate key dynamical aspects of the system that were not previously addressed. Specifically, we establish the existence and uniqueness of solutions using the fixed point theorem, perform sensitivity analysis of the basic reproduc tion numbers for both diseases to identify key epidemiological parameters driving disease transmission, and formulate an optimal control problem to determine effective intervention strategies. Furthermore, numerical simulations are carried out using Python to illustrate the theoretical results and to provide insight into the impact of control measures on disease dynamics. The results obtained provide deeper understanding of the model behavior and offer useful guidance for designing efficient strategies to mitigate the co-infection burden of COVID-19 and Monkeypox.