Fractal and Fractional, Volume 9, Issue 8

Fractal theory provides a powerful tool for quantifying complex geometric patterns such as concrete cracks. The box-counting method is widely employed for fractal dimension (FD) calculation due to its intuitive principles and compatibility with image...

Using the newly introduced, by the author, basic complex and hybrid complex rheologic models of the fractional type, the dynamics of a series of mechanical rheologic discrete dynamical systems of the fractional type (RDDSFT) of rheologic oscillators...

We are especially interested in the general framework and ability of a semi-analytic method (SAM) to use the trigonometric basis function (TBF) in different domains. Moreover, the stabilizing effect of increasing boundary nodes on the convergence of...

This paper presents a comprehensive dynamical analysis of a nonlinear oscillator subjected to both deterministic and stochastic excitations. Utilizing a diverse suite of analytical tools—including phase portraits, Poincaré sections, Lyap...

This study focuses on a hydrocarbon reservoir located in southeastern Mexico. The analysis uses well log data derived from petrophysical evaluations of storage capacity. The structural complexity of the reservoir and observed heterogeneity in Cretace...

The novelty herein pertains to a class of fractional differential equations involving the Hadamard fractional derivative of higher order. Our investigation encompasses the fractional integral operator of a logarithmic function. The mathematical tools...

The inherent randomness and concealment of rumors in social networks exacerbate their spread, leading to significant societal instability. To explore the mechanisms of rumor propagation for more effective control and mitigation of harm, we propose a...

Rod pump systems are complex nonlinear processes, and conventional efficiency prediction methods for such systems typically rely on high-order fractional partial differential equations, which severely constrain real-time inference. Motivated by the i...

This paper studies the large deviation principle (LDP) of a class of Hilfer fractional stochastic McKean–Vlasov differential equations with multiplicative noise. Firstly, by making use of the Laplace transform and its inverse transform, the sol...

This study presents a comprehensive grayscale texture analysis framework for investigating the microstructural evolution of cement-based materials during hydration. High-resolution X-ray computed tomography (X-CT) slice images were analyzed across fi...