Fractional calculus, albeit a synonym of fractional integrals and derivatives which have two
main characteristics—singularity and nonlocality—has attracted increasing interest due to its …

We introduce a sampling-based machine learning approach, Monte Carlo fractional physics-
informed neural networks (MC-fPINNs), for solving forward and inverse fractional partial …

This paper proposes the stiffness nonlinearities and asymmetric SD (smooth and
discontinuous) oscillator under time-delayed feedback control with the fractional derivative …

We study the dynamic evolution of COVID-19 caused by the Omicron variant via a fractional
susceptible–exposed–infected–removed (SEIR) model. Preliminary data suggest that the …

We analyze a plurality of epidemiological models through the lens of physics-informed
neural networks (PINNs) that enable us to identify time-dependent parameters and data …

A class of tempered fractional differential equations with terminal value problems are
investigated in this paper. Discretized collocation methods on piecewise polynomials …

In this paper, we study the Caputo–Hadamard fractional partial differential equation where
the time derivative is the Caputo–Hadamard fractional derivative and the space derivative is …

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In this paper, we study the stability and logarithmic decay of the solutions to fractional
differential equations (FDEs). Both linear and nonlinear cases are included. And the …

Lyapunov exponents provide quantitative evidence for determining the stability and
classifying the limit set of dynamical systems. There are several well-established techniques …