Fractional-order differential equations are powerful tools for the representation of dynamic systems that exhibit long-term memory effects. The verified simulation of such system models with the help of interval tools allows for the computation of gu...
Verified simulation techniques have been investigated intensively by researchers who are dealing with ordinary and partial differential equations. Tasks that have been considered in this context are the solution to initial value problems and boundary...
In this article, we delve into delayed fractional differential equations with Riemann–Stieltjes integral boundary conditions and fractional impulses. By using differential inequality techniques and some fixed-point theorems, some novel sufficie...
In this study, we prove the existence and uniqueness of a best proximity point in the setting of non-Archimedean modular metric spaces via the concept of simulation functions. A non-Archimedean metric modular is shaped as a parameterized family of cl...
Fractional Stochastic Differential Equations are becoming more popular in the literature as they can model phenomena in financial data that typical Stochastic Differential Equations models cannot. In the formulation considered here, the Hurst paramet...
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We investigate a class of fractional time-partial differential equations describing the dynamics of the fast action potential process in contractile myocytes. The system is explored in both one and two dimensional cases. Homogeneous and nonhomogeneou...
In this paper, we present a control problem related to a semilinear differential equation with a moving singularity, i.e., the singular point depends on a parameter. The particularity of the controllability condition resides in the fact that it depen...
This paper examines the existence and stability of an m-cyclic coupled system of higher-order fractional differential equations with non-singular kernels. Sufficient conditions for the existence and stability of solutions are obtained using fixed-poi...
This paper proposes an approximation algorithm based on the Legendre and Chebyshev artificial neural network to explore the approximate solution of fractional Lienard and Duffing equations with a Caputo fractional derivative. These equations show the...
In this study, random-order FDEs are studied with a focus on the variability of their solutions and random orders when the order of differentiation is governed by a probability distribution. Fractional differential equations (FDEs) offer a generalize...
In this paper, we consider numerical solutions for a general form of fractional delay differential equations (FDDEs) with fractional derivatives defined in the Caputo sense. A fractional integration operational matrix, created using a fractional Tayl...
N2 huff-n-puff has proven to be a promising technique to further improve oil recovery in naturally fractured-cavity carbonate reservoirs. The effect of enhanced oil recovery (EOR) by N2 huff-n-puff is significantly affected by various dynamic and sta...
The exact solution to fractional-order partial differential equations is usually quite difficult to achieve. Semi-analytical or numerical methods are thought to be suitable options for dealing with such complex problems. To elaborate on this concept,...
The main aim of this paper is to suggest an algorithm for constructing two monotone sequences of mild lower and upper solutions which are convergent to the mild solution of the initial value problem for Riemann-Liouville fractional delay differential...
Accurate mapping of electromagnetic field distributions is crucial in the analysis and design of electromechanical devices such as electric machines. Fractional calculus is a tool currently under development that allows classical models to be general...
This study introduces a novel Fuzzy Piecewise Fractional Derivative (FPFD) framework to enhance epidemiological modeling, specifically for the multi-phasic co-infection dynamics of Omicron and malaria. We address the limitations of traditional models...
We introduce a class of triply coupled systems of differential equations with fractal–fractional Caputo derivatives and time-dependent delays. This framework captures long-memory effects and complex structural patterns while allowing delays to...
Fractional-order models are widely recognized for their ability to capture memory and hereditary effects in biological and physiological systems. In this paper, we develop and analyze a Caputo fractional-order dynamical model for the regulation of bl...
The present work is concerned with the study of a generalized Langevin equation and its link to the physical theories of statistical mechanics and scale relativity. It is demonstrated that the form of the coefficients of the Langevin equation depends...
This Special Issue invited researchers to contribute their original research work and review articles on “Symmetry and Fluid Mechanics” that either advances the state-of-the-art mathematical methods through theoretical or experimental stu...
Fractional-order proportional–integral–derivative (FOPID) control offers additional tuning freedom, but a controller selected in an ideal or averaged model may not remain preferable after circuit realization and switching-level evaluation...
This paper applies a recently proposed numerical algorithm to discuss the deflection of viscoelastic micro-beams in the time domain with direct access. A nonlinear-fractional order model for viscoelastic micro-beams is constructed. Before solving the...
This paper presents a generalized epidemic modeling framework based on g-tempered Caputo fractional derivatives with discrete time delays. The proposed approach incorporates nonlocal memory effects, nonlinear temporal scaling, and delayed epidemiolog...
The fractional Legendre polynomials (FLPs) that we present as an effective method for solving fractional delay differential equations (FDDEs) are used in this work. The Liouville–Caputo sense is used to characterize fractional derivatives. This...
The fractional calculus is a specific case of classical calculus, as is well known [...]
This paper pursues obtaining Jacobi spectral collocation methods to solve Caputo fractional differential equations numerically. We used the shifted Jacobi–Gauss–Lobatto or Jacobi–Gauss–Radau quadrature nodes as the collocation...
The present study uses linear quadratic regulator (LQR) theory to control a vibratory system modeled by a fractional-order differential equation. First, as an example of such a vibratory system, a viscoelastically damped structure is selected. Second...
In this article, an attractive numeric–analytic algorithm, called the fractional residual power series algorithm, is implemented for predicting the approximate solutions for a certain class of fractional systems of partial differential equations in t...
The Riesz space-fractional derivative is discretized by the Fourier pseudo-spectral (FPS) method. The Riesz space-fractional nonlinear Klein–Gordon–Zakharov (KGZ) and Klein–Gordon–Schrödinger (KGS) equations are transform...
In this paper, we studied a fractional-order robust backstepping control (BSC) combined with a fractional-order tracking differentiator and a fractional-order nonlinear disturbance observer for a quadrotor unmanned aerial vehicle (UAV) system. A frac...
This study explores the application of advanced mathematical techniques to solve fractional differential equations, focusing particularly on the fractional diffusion equation. The fractional diffusion equation, used to simulate a range of physical an...
In this research, we present a new computational technique for solving some physics problems involving fractional-order differential equations including the famous Bagley–Torvik method. The model is considered one of the important models to sim...
Numerical simulation of physical issues is often performed by nonlinear modeling, which typically involves solving a set of concurrent fractional differential equations through effective approximate methods. In this paper, an analytic-numeric simulat...
This paper presents an integer and fractional-order Park’s model of a wound-rotor induction motor with a three-phase eddy-current starter incorporated into the rotor circuit. The integer-order model is described by differential equations with i...
A mathematical model of the anomalous diffusion of surfactant and the process of adsorption–desorption on an interface is analyzed using a fractional calculus approach. The model is based on time-fractional partial differential equations in the...
This research focuses on the analysis of the competitive model used in the banking sector based on the stochastic fractional differential equation. For the approximate solution, a pseudospectral technique is utilized for the proposed model based on t...
Despite the existence of a secure and reliable immunization, measles, also known as rubeola, continues to be a leading cause of fatalities globally, especially in underdeveloped nations. For investigation and observation of the dynamical transmission...
This article investigates the differential privacy of the initial state for nabla discrete fractional-order dynamic systems. A novel differentially private Gaussian mechanism is developed which enhances the system’s security by injecting random...
This paper consists of a general consideration of a seismic system as a subsystem of another, larger system, exchanging with it by extensive dynamical quantities in a sequential push mode. It is shown that, unlike an isolated closed system described...
The harmonic oscillator is a fundamental physical–mathematical system that allows for the description of a variety of models in many fields of physics. Utilizing fractional derivatives instead of traditional derivatives enables the modeling of...
A primary aim of this study is to examine and simulate a fractional Coronavirus disease model by providing an efficient method for solving numerically this important model. In the Liouville-Caputo sense, the examined model consists of five fractional...
This paper deals with a new class of hybrid fractional differential equations with fractional proportional derivatives of a function with respect to a certain continuously differentiable and increasing function
In this paper, the averaging principle for Caputo type fractional stochastic differential equations with Lévy noise is investigated with consideration of a new method for dealing with singular integrals. Firstly, the estimate on higher moments...
Two-dimensional advection–diffusion processes with memory and a source concentrated in the symmetry center of the domain have been investigated. The differential equation of the studied model is a fractional differential equation with short-tai...
The telegraph equation is a hyperbolic partial differential equation that has many applications in symmetric and asymmetric problems. In this paper, the solution of the time-fractional telegraph equation is obtained using a hybrid method. The numeric...
Fractional calculus approach is used to analyze the model of surfactant transport by anomalous diffusion and its adsorption on an interface in a liquid-liquid system. The anomalous diffusion is modeled by time-fractional partial differential equation...
The fractional differential equation has a memory property and is suitable for biomathematical modeling. In this paper, a fractional SEQIR epidemic model with saturated incidence and vaccination is constructed. Firstly, for the deterministic fraction...
Ordinary differential equations have recently been extended to fractional equations that are transformed using fractional differential equations. These fractional equations are believed to have high accuracy and low computational cost compared to ord...
In this paper, we introduce a new Caputo-type modification of the Erdélyi–Kober fractional derivative. We pay attention to how to formulate representations of Erdélyi–Kober fractional integral and derivatives operators. Then, some properties of the n...
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