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A Reduced-Order Finite Difference Scheme Based on POD for Fractional Stochastic Advection–Diffusion Equation
This article introduces a new scheme for the fractional stochastic advection–diffusion equation (FSA-DE) in time where the fractional term is...
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Visual double image encryption scheme based on multilayer complex networks and wavelet transform
This paper explores the synchronizability within a three-layer network, which has the feature of identical topologies across layers but with three...
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Some Integral Transform Results for Hilfer–Prabhakar Fractional Derivative and Analysis of Free-Electron Laser Equation
In this paper, Natural transforms of Prabhakar integral, Hilfer–Prabhakar (HP) fractional derivative and regularized Caputo form of HP fractional...
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Numerical solutions of fractional differential equation with multiple delays via block boundary value method
The aim of this paper is to present a new numerical scheme, namely the fractional multi-delay block boundary value method (FMDBBVM), which is...
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Numerical solution of time-fractional telegraph equations using wavelet transform
This study solves the time-fractional telegraph equations with Dirichlet boundary conditions using a novel and effective wavelet collocation method...
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Combined Synchronization for Fractional-Order Chaotic Systems with Time Delay
Stability is the core problem of chaotic system synchronization control. There are far fewer tools to judge the stability of fractional delay...
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Modeling Klebsiella pneumonia infections and antibiotic resistance dynamics with fractional differential equations: insights from real data in North Cyprus
This study presents an enhanced fractional-order mathematical model for analyzing the dynamics of Klebsiella pneumonia infections and antibiotic...
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A spectral shifted gegenbauer collocation method for fractional pantograph partial differential equations and its error analysis
This study presents a new numerical approach for solving fractional-order pantograph partial-differential equations, in which the fractional...
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New theories and applications of tempered fractional differential equations
In this paper, we develop theories, properties and applications of a new technique in tempered fractional calculus called the Tempered Fractional...
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A New Approach for Optical Image Encryption Standard Using Bit Swap** and Fractional Fourier Transform
Because of the exponential evolution of digital knowledge, cloud, Internet of things (IoT) technologies, personal information protection and security...
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The Comparative Study of Time Fractional Linear and Nonlinear Newell–Whitehead–Segel Equation
In this study, the homotopy analysis method (HAM) and fractional reduced differential transform method (FRDTM) are executed to solve the...
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Algorithmic Complexity-Based Fractional-Order Derivatives in Computational Biology
Fractional calculus approach, providing novel models through the introduction of fractional-order calculus to optimization methods, is employed in...
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High-Precision Method for Space-Time-Fractional Klein-Gordon Equation
This paper presents the space-time fractional Klein-Gordon equations (FKGEs) for the spinless particle in potential field. It defines to describe the...
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Time-fractional Landau–Khalatnikov model applied to numerical simulation of polarization switching in ferroelectrics
Ferroelectrics are complex structured media that exhibit fractal properties and memory effects in terms of a number of dynamic characteristics. The...
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Time Fractional Heat Equation of n + 1-Dimension in Type-1 and Type-2 Fuzzy Environment
Typically, the parameters of a practical problem are considered to be deterministic. Nevertheless, there may be possibility that these parameters are...
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Novel patterns in the space variable fractional order Gray–Scott model
In this paper, we apply Fourier spectral method to simulate the process of pattern formations of the space variable fractional order Gray–Scott...
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Fractional Order Control of Three-Phase Four-Wire Inverters Under Unbalanced and Nonlinear Load Conditions
In this paper, a novel control scheme is proposed to regulate the three-phase output line-to-neutral voltages of a three-phase split-capacitor...
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Approximation of Fractional-Order Systems Using Balanced Truncation with Assured Steady-State Gain
This research presents a novel and stable approach for reducing the order of fractional-order systems using the advantage of a balanced truncation...
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Generalized fractional-order hygro-thermo-viscoelastic wave propagation/reflection in annular spinning discs: comparisons with the classical and Lord–Shulman thermo-viscoelastic models
Propagation, reflection, and interference of the hygro-thermo-viscoelastic temperature, displacement, and stress waves are investigated here in...
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Fractional-Order Adaptive SMC for the Deployment of STS
In this chapter, a novel FO SMC scheme based on a nonlinear mathematical model in elliptical orbits is presented. A new dimensionless transform based...