Fractal and Fractional, Volume 9, Issue 1

This paper presents a new SIRS model for recurrent childhood diseases under the Caputo fractional difference operator. The existence theory is established using Brouwer’s fixed-point theorem and the Banach contraction principle, providing a com...

This article investigates the continuity of derivatives of real-valued functions from a topological perspective. This is achieved by the characterization of their sets of discontinuity. The same principle is applied to Gateaux derivatives and gradien...

Doppler shift estimation continues to be a critical challenge of utmost significance in both theoretical research and practical engineering applications. Many innovators have crafted solutions specific to this issue, with notable contributions across...

This paper develops integral inequalities for first-order differentiable convex functions within the framework of fractional calculus, extending Boole-type inequalities to this domain. An integral equality involving Riemann–Liouville fractional integ...

To study the influence of the spatial distribution and structure of multi-scale cracks on the mechanical behavior of rocks, triaxial compression tests and cyclic triaxial complete loading and unloading tests were conducted on sandstone, with real-tim...

The proposed study seeks to investigate various analytical and numerical techniques for solving fractional differential equations, with a particular focus on their applications in mathematical modeling and scientific research within the field of alge...

To analyze the pore structure and fractal characteristics of marine shale in the lower Cambrian Niutitang Formation in northwestern Hunan Province, China, the pore characteristics of shale were characterized using total organic carbon (TOC) content,...

Finding the relevant scale to observe the influence of a process is one of the most important purposes of multiscale surface characterization. This study investigates various methods to determine a pertinent scale for evaluating the relationship betw...

This article investigates the problem of finite-time synchronization of fractional-order complex-valued random multi-layer networks without decomposing them into two real-valued systems. Firstly, by promoting real-valued signum functions, sign functi...

This article addresses a new class of delayed fractional multivalued problems complemented with nonlocal boundary conditions. In view of infinite delay theory, we convert the inclusion problem into a fixed-point multivalued problem, defined in an app...

This study examines a Caputo-type fractional-order food chain model, considering the Holling type II functional response with the vigilance effect. The model explores the interaction dynamics of the food chain model, which consists of prey, middle pr...

The one-time completion blasting technology for blind shafts is widely used in underground mining, for safety reasons. Efficient blind shaft excavation relies on reasonable cutting blasting technology. To optimize blasting parameters, the impact of e...

This paper presents an algorithm for solving the inverse fractional Stefan problem. The considered inverse problem consists of determining the heat transfer coefficient at one of the boundaries of the considered region. The additional information nec...

The objective of this paper is to demonstrate the existence and uniqueness (EU) of solutions to a class of Fractional Integro-Stochastic Differential Equations (FISDEs) by utilizing the fixed-point technique (FPT) and stochastic techniques. Additiona...

In this paper, a discrete-time design of a fractional internal model-based repetitive controller with a sliding mode approach is presented for uncertain linear systems subject to repetitive trajectory and periodic disturbance. The proposed algorithm,...

This study presents an innovative iterative method designed to approximate common fixed points of generalized contractive mappings. We provide theorems that confirm the convergence and stability of the proposed iteration scheme, further illustrated t...

The finite-time cluster synchronization (FTCS) of fractional-order complex-valued (FOCV) neural network has attracted wide attention. It is inconvenient and difficult to decompose complex-valued neural networks into real parts and imaginary parts. Th...

Power-law, inverse exponential and logarithmic models are widely used as empirical tools to describe anomalies in spatial and temporal geodynamic processes. However, the lack of clear interpretation of the relationships and distinctions among these m...

This paper introduces interpolative enriched cyclic Reich–Rus–Ćirić operators in normed spaces, expanding existing contraction principles by integrating interpolation and cyclic conditions. This class of operators addresses mapp...

This work is devoted to the hyperbolic sine function (HSF) control-based finite-time bipartite synchronization of fractional-order spatiotemporal networks and its application in image encryption. Initially, the addressed networks adequately take into...

This study presents a novel Fractional Whale Optimization Algorithm-Enhanced Support Vector Regression (FWOA-SVR) framework for solar energy forecasting, addressing the limitations of traditional SVR in modeling complex relationships within data. The...

Fractional electrodamage in A549 human lung cancer cells was analyzed by introducing a non-integer order parameter to model the influence of electrical stimulation on cellular behavior. Numerical simulations were conducted to evaluate the conversion...

Series arc faults (SAFs) pose a significant threat to the safety of photovoltaic (PV) systems. However, the complex operating conditions of PV systems make accurate SAF detection challenging. To tackle this issue, this article proposes a SAF detectio...

This study investigates the impact response of polymer foams commonly used in protective packaging, considering the fractal nature of their material microstructure. The research begins with static material characterization and impact tests on two low...

A nonlinear $(3+1)$-dimensional nonlinear Geng equation that can be utilized to explain the dynamics of shallow-water waves in fluids is given special attention. Various wave solutions are produced with the aid of the Hirota bilinear and Cole–Hop...

Recent research on fractional-order cascaded H-bridge multilevel static compensator (FCHM-STATCOM) indicates that it has better performance than the traditional cascaded H-bridge multilevel static compensator (CHM-STATCOM). The existing FCHM-STATCOM...

This article presents a printed antenna, designed with a fractal-shaped patch with fish-tail structured outer edges, a tapered feedline, and a rectangular notch-based defected partial ground structure (DPGS). The presented design has been printed on...

In this work, we propose and investigate a model of the dynamical behavior of HIV/AIDS transmission by considering a new compartment of the population with HIV: the latent asymptomatic class. The infection reproduction number that stabilizes the glob...

Complexity evaluation of hydro-climatic datasets is a challenging but essential pre-requisite for accurate modeling and subsequent planning. Changes in climate and anthropogenic interventions amplify the complexity of hydro-climatic time-series. Unde...

Granular soil is a porous medium composed of particles with different sizes and self-similar structures, exhibiting fractal characteristics. It is well established that variations in these fractal properties, such as particle size distribution (PSD),...

This paper introduces a new identity involving fractal–fractional integrals, which allow us to derive several new Bullen-type inequalities via generalized convexity. This study provides a significant advancement in the area of fractal–fra...

Cosmic rays exhibit anomalous diffusion behaviors in the heliospheric environment that cannot be adequately described by classical diffusion models. In this paper, we develop a theoretical framework employing a fractional Fokker–Planck equation...

The aim of this article is to introduce analytical and approximate techniques to obtain the solution of time-fractional Navier–Stokes equations. This proposed technique consists is coupling the homotopy perturbation method (HPM) and Laplace tra...

Fractional calculus (or arbitrary order calculus) refers to the integration and derivative operators of an order different than one and was developed in 1695. They have been widely used to study dynamical systems, especially chaotic systems, as the u...

This paper presents a novel Fuzzy Logic Controller (FLC) framework aimed at enhancing the performance and stability of Automatic Voltage Regulators (AVRs) in power systems. The proposed system combines fuzzy control theory with the Fractional Order P...

This paper presents an analysis of the existence, uniqueness, and stability of solutions to fractional neutral Volterra-Fredholm integro-differential equations, incorporating Caputo fractional derivatives and semigroup operators with state-dependent...

The article is devoted to the study of economic cycles and crises, which are studied within the framework of the theory of N.D. Kondratiev long waves (K-waves). The object of the study is the fractional mathematical models of S. V. Dubovsky, consisti...

In this paper, an incommensurate fractional-order chaotic system is established based on Chua’s system. Combining fractional-order calculus theory and the Adomian algorithm, the dynamic phenomena of the incommensurate system caused by different...

The adsorption of coalbed methane alters the pore structure of reservoirs, subsequently affecting the coal seam’s gas adsorption capacity. However, traditional gas adsorption models often neglect this crucial aspect. In this article, we introdu...

In this article, we focused on the fractional order modeling, simulations and neural networking to observe the correlation between severity of infection in HIV-AIDS patients and the role of treatments and control. The model is structured with eight c...

This paper has addressed the terrain-following problem of an autonomous underwater vehicle for widely used ocean survey missions. Considering the terrain feature description with limited sensing ability in underwater scenarios, a vertically installed...

Understanding cross-correlation and information flow between stocks is crucial for stock market analysis. However, traditional methods often struggle to capture financial markets’ complex and multifaceted dynamics. This paper presents a robust...

To study the effects of rock models with different fractal dimensions on their mechanical properties and fracture behavior, three representative numerical rock models, including the digital texture model, the Voronoi polygon model, and the Weibull di...

The wetting behavior of shale oil and gas on shale surfaces is determined by the interplay of organic matter (OM), mineral composition, and the intricate pore network structure of the shale. In this paper, the sensitivity responses of the Frenkel&nda...

With the evolution of unconventional oil and gas exploration concepts from source rocks and reservoirs to carrier beds, the inter-layer sandstone carrier bed within marine–continental transitional shale strata has emerged as a significant targe...

This paper explores a significant fractional model, which is the fractional Lakshamanan–Porsezian–Daniel ($\mathcal{FLPD}$) model, widely used in various fields like nonlinear optics and plasma physics. An advanced analytical solution for it is attai...

By analyzing reconstructed three-dimensional images of retinal bipolar neurons, we show that their dendritic arbors weave through space in a manner that generates fractal-like behavior quantified by an ‘effective’ fractal dimension. Exami...

Conventional cancer drugs are small molecules that target specific pathways. We introduced PCMS, a 26 kDa supramolecule combining sensors (S), molecular motors (M), and switching molecules (C), integrated within a fourth-generation PAMAM structure (P...

This paper focuses on the existence and uniqueness of solutions for $\vartheta$-fractional stochastic integral equations ($\vartheta$-FSIEs) using the Banach fixed point theorem (BFPT). We explore the Ulam–Hyers stability (UHS) of $\vartheta$-FSIE...

This study investigates the asymptotic behavior of non-oscillatory solutions to forced-perturbed fractional differential equations with the Caputo fractional derivative. The main aim is to unify the Beta Integral Lemma (Lemma 2) and the Gamma Integra...