Fractal and Fractional, Volume 10, Issue 5

The deep marine shale of the Wufeng–Longmaxi (WF–LMX) Formation in the Sichuan Basin is characterized by laterally continuous thickness, high porosity, and significant gas content, making it a representative shale reservoir with considera...

In this article, we investigate the existence of solutions for a class of fractional integro-differential equations (FIDE’s) involving the $\psi$-Caputo fractional derivative ($\psi$-CFD) subject to $\psi$-Caputo boundary conditions. The analysis...

In this paper, a finite difference scheme is proposed for the variable-order time-fractional sub-diffusion equation, achieving second-order accuracy in time and sixth-order accuracy in space. For spatial discretization, a newly constructed operator $\mathcal{A}$...

In this study, a fractional-order epidemic compartmental model is formulated using the Caputo derivative to account for the memory effects of the chikungunya virus. Based on Banach contractions, fixed-point theorems are used to prove existence and un...

This paper proposes a parametrization transform method for model-unknown networked control systems by using a data-driven event-triggered scheme. The key contribution is that an easy-to-apply parametrization transform method is proposed to convert th...

In this paper, we investigate the practical exponential stability of a class of nonlinear systems governed by the tempered $\varpi$-Caputo fractional derivative. A new Lyapunov-based criterion is established to derive sufficient conditions ensuring $\mathrm{\&piv}$...

The security of heterogeneous unmanned systems (HUSs) operating in open environments has become a key concern. Therefore, this paper focuses on the fractional-order adaptive resilient clustering synchronization control for a class of networked HUSs c...

Gearbox fault diagnosis under controlled bench-test conditions with known speed variations and noise interference remains challenging because nonstationarity, background noise, and operating-condition fluctuations can easily submerge weak localized f...

In this paper, new generalizations of Newton-type inequalities for the class of strongly convex functions by utilizing Riemann–Liouville fractional integrals are established. New estimates are obtained for functions that are strongly convex. Th...

Nonlinear equations arise extensively in engineering and applied sciences, where efficient and reliable iterative solvers are required. This study introduces two fractional-order iterative schemes based on a common predictor–corrector structure...

In this paper, an efficient numerical framework combined with RK4 method and Richardson extrapolation is proposed to solve nonlinear time-dependent partial differential equations involving the Riesz fractional Laplacian operator ${(-\Delta )}^s$. Th...

Solving fractional differential equations using spectral collocation methods based on classical orthogonal polynomials often leads to a reduced convergence rate due to the limited regularity of the solutions. Therefore, spectral collocation methods t...

This paper addresses the existence of mild solutions and the approximate controllability of a class of higher-order Hilfer fractional semi-linear neutral stochastic differential equations with non-instantaneous impulses in Hilbert spaces. The system...

In this study, we obtain new Hermite–Hadamard type inequalities involving an extended form of the Atangana–Baleanu fractional integral operator having Mittag-Leffler kernels. The approach is based on a suitable integral identity for diffe...

In this article, we use truncated M-fractional derivatives to analyze the bifurcation and chaotic behavior of and traveling-wave solutions to the Zhiber–Shabat equation. By introducing truncated M-fractional derivatives, the equation exhibits r...

In this paper, we propose and numerically investigate a fractional T system. As a fractional generalization of the classical T model, the fractional order serves as a memory parameter governing the system dynamics. By employing the fractional stabili...

The growing complexity of modern decision-making environments, characterized by multi-dimensional data, uncertainty, and dynamic behavior, demands advanced mathematical frameworks for effective information aggregation. Although fractional fuzzy tenso...

This study focuses on establishing the existence and uniqueness of solutions for nonlinear fractional differential equations through the application of fixed-point methods in complex-valued suprametric spaces. In order to accomplish this, novel cycli...

Accurate battery state-of-health (SOH) estimation is essential for safe and reliable electric-vehicle operation. This paper presents a Tempered Fractional Deterministic Learning (TF-DL) framework that combines deterministic learning with a tempered f...

Fractional-order controllers have emerged as robust alternatives to conventional PID controllers. Existing tuning methods generally focus solely on robustness to process gain variations. This paper introduces a design method for fractional-order PI c...

Understanding the pore structure of high-rank coals is essential in evaluating gas storage and transport. Here, twelve semianthracite samples from the early Permian Shanxi Formation were investigated by proximate analysis, optical microscopy, low-tem...

We study a perturbed coupled system of generalized hybrid pantograph equations involving the deformable derivative of Zulfeqarr–Ujlayan–Ahuja. A central point of the revision is made explicit: for classically differentiable functions this...

This article employs a fractional differential equation model to probe the dynamic mechanism of animal avoidance learning and memory retention. This model encompasses both linear and nonlinear scenarios. We first obtain the series-type analytical sol...

Understanding the multifractal dynamics of carbon and energy markets is essential for capturing complex cross-market interactions and policy-induced volatility. This study investigates China’s carbon and energy markets from 16 July 2021 to 30 J...

Within the framework of elastoplastic theory, this study develops and improves a fractional cyclic constitutive model capable of describing rate-dependent ratcheting behavior by defining the ratcheting parameter as a function of the cumulative plasti...

We develop a high-order space-time spectral method for nonlinear convection–diffusion equations with a Riemann–Liouville time-fractional derivative and a spectrally defined space-fractional Laplacian. The spatial discretization uses a Fou...

In this paper, we establish Lyapunov-type and Hartman–Wintner-type integral inequalities for boundary value problems involving a class of composite fractional integral operators. By employing an explicit Green function representation and sharp...

Accurate wind speed prediction is essential for wind power generation and wind-resistant structural design. In this research, a short-term wind speed prediction model that combines the wavelet decomposition (WD) method and a fractal-based long short-...

Fractional-order operators play a fundamental role in the modeling and control of complex dynamical systems; however, their infinite-dimensional nature necessitates rational approximation for practical implementation. This paper presents a unified co...

Diabetes mellitus is a chronic disease with complex progression dynamics. This study introduces a fractional order compartmental model based on the Caputo derivative, a singular-kernel derivative, to describe disease progression across four compartme...

Time–frequency analysis (TFA) facilitates the extraction of instantaneous frequency (IF) features from non-stationary signals. Transient Extraction Transform (TET) produces highly concentrated time–frequency representations (TFRs) for pul...

Reservoir evaluation and interpretation are fundamental for production and reserve management, and they require, as a key input, an information matrix describing petrophysical properties within the static model. This study provides the scalar distrib...

Accurate description of phase change heat transfer in porous media relies on precise characterization of pore structures. In this study, fractal theory is employed to characterize the complex microstructure and pore distribution of metallic foams, an...

This paper investigates a class of boundary value problems involving Caputo fractional derivatives of order $\nu \in (2,3]$. We begin by establishing two novel comparison principles. Subsequently, by employing the monotone iterative technique co...

This paper investigates the leader–follower consensus problem for fractional-order nonlinear multi-agent systems operating under simultaneous Sybil and Denial-of-Service (DoS) attacks. The communication topology is modeled as a time-varying dir...

Population-based metaheuristic algorithms are widely used for multi-objective city evacuation planning, yet their opaque internal dynamics limit practitioner trust in safety-critical contexts. This study introduces, to the best of our knowledge, the...

The theory of analytic functions remains a fundamental area of geometric function theory, with particular emphasis on coefficient problems, differential subordinations, and determinant estimates. Motivated by recent developments in fractional calculu...

This paper introduces a novel memristor-based hyperchaotic system in which the integer-order derivatives are replaced by a variable-order fractal-fractional operator. The dynamical properties of the system, including equilibrium points, Lyapunov expo...

We investigate the multifractal structure of unstable local polynomial entropies for arbitrary Borel probability measures in partially hyperbolic dynamical systems. We introduce the notions of Bowen unstable polynomial entropy, unstable local polynom...

By constructing two distinct Lyapunov-like functions and employing concepts of $\alpha$-/$\omega$-limit sets, this article reinvestigates the Caputo fractional-order ($0<\alpha \le 1$) memristor-based Lorenz system, and rigorously proves that there ex...

Human motivation is governed by a long-memory cognitive process in which the depth of temporal integration—how far into the past the system draws upon accumulated experience—is not fixed, but dynamically compressed under cognitive stress....

The long-term stability of rock–concrete composites largely depends on the mechanical properties and durability of the rock–concrete interface. This study investigated the coupling effect of interfacial roughness and acid sulfate corrosio...

The Gulong shale oil reservoir is characterized by high clay content and strong heterogeneity, with substantial variations in mineral composition among different intervals. However, existing fracability evaluation methods for such continental shales...

Fractals represent one of the fundamental manifestations of complexity, and fractal networks serve as tools for characterizing and investigating the fractal structures and properties of large-scale systems. Higher-order networks have emerged as a res...

This work explores the growing field of fractional calculus, with particular emphasis on the complexities and opportunities associated with variable-order derivatives. We critically assess existing definitions, identifying those that are consistent w...

This paper investigates a discrete-time fractional-order predator–prey model incorporating a double Allee effect in the prey population, derived from a fractional differential system via the piecewise constant argument method to capture both me...

Thisarticle develops and analyzes a fractional-order Leslie–Gower prey–predator–parasite system incorporating two discrete delays and nonlocal spatial diffusion. The model’s central novelty lies in the simultaneous integration...

This paper investigates the existence, uniqueness, and stability of solutions for a new class of coupled systems of sequential fractional differential equations involving the Hilfer fractional derivative. Generalizing previous works based on Caputo d...

Resistivity is a key parameter in shale reservoir characterization. Diverse micro-pore types and complex conduction mechanisms in shale result in poor accuracy when applying existed conductivity models. Establishing a high-precision conductivity resp...

This paper presents a novel proportional–integral–derivative (PID) control framework for first $\alpha$-order systems evolving in fractal time. The main contribution is the extension of classical control theory to systems exhibiting anomal...