☆ 4.7 Article

Fractional Diffusion Equation under Singular and Non-Singular Kernel and Its Stability

FRACTAL AND FRACTIONAL (2023)

Related references

Note: Only part of the references are listed.

Article Computer Science, Interdisciplinary Applications

Discretised general fractional derivative

Enyu Fan et al.

Summary: A generalised fractional derivative (the psi-Caputo derivative) is studied and generalisations of standard discretisations are constructed. Numerical examples are given to demonstrate their performance, showing their extension to known results for the standard Caputo derivative, the Caputo-Hadamard derivative, etc.

MATHEMATICS AND COMPUTERS IN SIMULATION (2023)

Add to Collection

Article Mathematics, Applied

An efficient ADI difference scheme for the nonlocal evolution problem in three-dimensional space

Haixiang Zhang et al.

Summary: This paper proposes a first-order fractional convolution quadrature scheme and backward Euler method for the numerical solution of the three-dimensional nonlocal evolution equation. By discretizing the second-order spatial derivative using the standard central finite difference approximation and using the alternating direction implicit method for three-dimensional problems, the computational cost is significantly reduced. The stability analysis and error bounds of the proposed method are provided. The effectiveness of the method is demonstrated through two test problems.

JOURNAL OF APPLIED MATHEMATICS AND COMPUTING (2023)

Add to Collection

Article Thermodynamics

Particle-scale heat and mass transfer processes during the pyrolysis of millimeter-sized lignite particles with solid heat carriers

Fangzhou Li et al.

Summary: The study investigates the mesoscale solid fuel pyrolysis behavior using a one-dimensional nonstationary model. The model incorporates a modified multistep kinetic model (MSM) and a series of heat and mass conservation equations, as well as a dusty gas model (DGM). The coupling effects between intraparticle transport processes and transient devolatilization kinetics are examined. The results reveal the emergence of notable multiphysical fields within lignite particles during pyrolysis, and the variation in volatiles transfer direction and mechanism. These factors significantly affect secondary reactions.

APPLIED THERMAL ENGINEERING (2023)

Add to Collection

Article Mathematics, Applied

A novel approach to investigate the stability analysis and the dynamics of reaction-diffusion SVIR epidemic model

Amer M. Salman et al.

Summary: Understanding the behaviour of nonlinear dynamical systems is crucial in epidemiological modelling. This paper investigates the stability analysis and dynamics of a reaction-diffusion SVIR model with partial immunity. Numerical simulation is performed to identify factors affecting the dynamics of the epidemiological model, highlighting the importance of transmission rates, vaccination, and treatment strategies. The use of numerical range techniques provides a comprehensive understanding of the eigenvalue spectrum, overcoming challenges associated with discretisation.

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION (2023)

Add to Collection

Article Mathematics, Applied

A space-time spectral order sinc-collocation method for the fourth-order nonlocal heat model arising in viscoelasticity

Xuehua Yang et al.

Summary: The purpose of this paper is to investigate a space-time Sinc-collocation method for solving the fourth-order nonlocal heat model arising in viscoelasticity, which exhibits weak singularities. The proposed method is balanced in both time and space variables and uses the Sinc-collocation method with SE transformation to deal with the initial singularity. The error bounds of the method show exponential convergence rate in space and time, and the experimental results confirm its precision and correctness.

APPLIED MATHEMATICS AND COMPUTATION (2023)

Add to Collection

Article Mathematics, Applied

An implicit robust numerical scheme with graded meshes for the modified Burgers model with nonlocal dynamic properties

Qingqing Tian et al.

Summary: In this paper, an implicit robust difference method is constructed to handle the modified Burgers model with nonlocal dynamic properties. The L1 formula on graded meshes is employed for the fractional derivative. The existence and uniqueness of numerical solutions are proved, and the unconditional stability is derived. A new discrete Gronwall inequality is introduced to improve the stability, and the optimal convergence order in the L-2 energy norm is also obtained. Numerical experiments demonstrate the efficiency of the proposed robust method on uniform and graded meshes.

COMPUTATIONAL & APPLIED MATHEMATICS (2023)

Add to Collection

Article Mathematics, Interdisciplinary Applications

A Predictor-Corrector Compact Difference Scheme for a Nonlinear Fractional Differential Equation

Xiaoxuan Jiang et al.

Summary: In this work, a predictor-corrector compact difference scheme is proposed to solve a nonlinear fractional differential equation. The MacCormack method is used to handle nonlinear terms, the Riemann-Liouville (R-L) fractional integral term is treated using the second-order convolution quadrature formula, and the Caputo derivative term is discretized using the L1 discrete formula. By calculating the first and second derivatives of the matrix under the compact difference, the precision of this scheme is improved. The existence and uniqueness are proven, and numerical experiments are presented.

FRACTAL AND FRACTIONAL (2023)

Add to Collection

Article Physics, Fluids & Plasmas

Fundamental solution of diffusion equation for Kappa gas: Diffusion length for suprathermal electrons in solar wind

M. H. Benetti et al.

Summary: A recent study analyzed data from the Parker Solar Probe to model the electron concentration in solar wind, finding a Kappa distribution with a spectral index of K=5. The researchers also developed a new class of non-linear partial differential equations to describe the diffusion of suprathermal gas, finding a spectral index of K>=1.5 for Kappa electrons in solar wind and suprathermal effects increasing the length scale of classical diffusion. The macroscopic formulation of their theory allows for future extensions, including magnetic fields and nonextensive statistics.

PHYSICAL REVIEW E (2023)

Add to Collection

Article Computer Science, Software Engineering

Numerical stability of Grunwald-Letnikov method for time fractional delay differential equations

Lei Li et al.

Summary: This paper investigates the numerical stability of F-DDEs based on the Grunwald-Letnikov approximation for the Caputo fractional derivative, focusing on the numerical stability region and Mittag-Leffler stability. Using the boundary locus technique, the exact expression of the numerical stability region in the parameter plane is derived. The study shows that the numerical solutions of F-DDEs differ significantly from classical integer order DDEs in terms of stability and long-time decay rate.

BIT NUMERICAL MATHEMATICS (2022)

Add to Collection

Article Mathematics, Applied

A robust error analysis of the OSC method for a multi-term fourth-order sub-diffusion equation

Haixiang Zhang et al.

Summary: In this paper, we propose an orthogonal spline collocation method to solve the fourth-order multi-term subdiffusion equation. The stability and convergence of the method are proved theoretically, and numerical results are provided to verify the effectiveness of the proposed method.

COMPUTERS & MATHEMATICS WITH APPLICATIONS (2022)

Add to Collection

Article Mathematics

Fractional Differential Equations with the General Fractional Derivatives of Arbitrary Order in the Riemann-Liouville Sense

Yuri Luchko

Summary: In this paper, the authors investigate the general fractional derivatives of arbitrary order defined in the Riemann-Liouville sense. They derive the explicit form of their null space and prove the second fundamental theorem of fractional calculus, which leads to a closed form formula for their projector operator. The authors also develop an operational calculus of the Mikusinski type for these derivatives and apply it to obtain explicit solutions to the corresponding fractional differential equations. These results provide important tools for solving these equations.

MATHEMATICS (2022)

Add to Collection

Review Engineering, Chemical

The Role of Diffusivity in Oil and Gas Industries: Fundamentals, Measurement, and Correlative Techniques

Ram R. Ratnakar et al.

Summary: This article discusses the mixing processes in multiphase fluid systems. In such systems, fluid/component mixing is complex and influenced by factors such as pressure, temperature, and time. Understanding these processes is crucial for the development of technologies that utilize these concepts, such as enhanced oil recovery and gas injection.

PROCESSES (2022)

Add to Collection

Article Nanoscience & Nanotechnology

A new approach for analysing interdiffusion in multicomponent alloys

Irina Belova et al.

Summary: The analysis of interdiffusion in multicomponent alloys is approached using a new mathematical method that fits composition profiles and determines interdiffusion coefficients. Small differences in composition profiles can lead to significant variations in interdiffusion coefficients. The new approach shows excellent performance in experimental results.

SCRIPTA MATERIALIA (2021)

Add to Collection

Article Mathematics, Interdisciplinary Applications

On a New Modification of the Erdelyi-Kober Fractional Derivative

Zaid Odibat et al.

Summary: The paper introduces a new Caputo-type modification of the Erdelyi-Kober fractional derivative, focusing on representations, properties, and relationships with other fractional derivatives. A numerical method is presented to deal with fractional differential equations involving the proposed modification, with the hope of widespread application in simulating fractional models.

FRACTAL AND FRACTIONAL (2021)

Add to Collection

Article Infectious Diseases

Early dynamics of transmission and control of COVID-19: a mathematical modelling study

Adam J. Kucharski et al.

LANCET INFECTIOUS DISEASES (2020)

Add to Collection

Article Physics, Multidisciplinary

Reaction-Diffusion Equation with Stationary Wave Perturbation in Weakly Ionized Plasmas

S. T. da Silva et al.

BRAZILIAN JOURNAL OF PHYSICS (2020)

Add to Collection

Article Physics, Multidisciplinary

Application of the diffusion equation to prove scaling invariance on the transition from limited to unlimited diffusion

Edson D. Leonel et al.

EPL (2020)

Add to Collection

Article Mathematics, Applied

Representations of acting processes and memory effects: General fractional derivative and its application to theory of heat conduction with finite wave speeds

Dazhi Zhao et al.

APPLIED MATHEMATICS AND COMPUTATION (2019)

Add to Collection

Article Multidisciplinary Sciences

Extensions and solutions for nonlinear diffusion equations and random walks

E. K. Lenzi et al.

PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES (2019)

Add to Collection

Article Mathematics, Applied

Fractional differential equations with a Caputo derivative with respect to a Kernel function and their applications

Ricardo Almeida et al.

MATHEMATICAL METHODS IN THE APPLIED SCIENCES (2018)

Add to Collection

Article Mathematics, Applied

von Neumann stability analysis of first-order accurate discretization schemes for one-dimensional (1D) and two-dimensional (2D) fluid flow equations

Santosh Konangi et al.

COMPUTERS & MATHEMATICS WITH APPLICATIONS (2018)

Add to Collection

Article Mathematics, Applied

Analysis of the fractional diffusion equations with fractional derivative of non-singular kernel

Mohammed Al-Refai et al.

ADVANCES IN DIFFERENCE EQUATIONS (2017)

Add to Collection

Article Geography, Physical

Weathering and erosion of fractured bedrock systems

Marina I. Lebedeva et al.

EARTH SURFACE PROCESSES AND LANDFORMS (2017)

Add to Collection

Article Mathematics, Applied

Modeling some real phenomena by fractional differential equations

Ricardo Almeida et al.

MATHEMATICAL METHODS IN THE APPLIED SCIENCES (2016)

Add to Collection

Article Mathematics, Interdisciplinary Applications

Dynamic Analysis of a Reaction-Diffusion Rumor Propagation Model

Hongyong Zhao et al.

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS (2016)

Add to Collection

Article Computer Science, Interdisciplinary Applications

Fractional Adams-Bashforth/Moulton methods: An application to the fractional Keller-Segel chemotaxis system

Mohsen Zayernouri et al.

JOURNAL OF COMPUTATIONAL PHYSICS (2016)

Add to Collection

Article Mathematics, Applied

A new predictor-corrector method for fractional differential equations

Varsha Daftardar-Gejji et al.

APPLIED MATHEMATICS AND COMPUTATION (2014)

Add to Collection

Article Mathematics, Interdisciplinary Applications

FINITE DIFFERENCE METHODS FOR FRACTIONAL DIFFERENTIAL EQUATIONS

Changpin Li et al.

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS (2012)

Add to Collection

Proceedings Paper Computer Science, Interdisciplinary Applications

Study of Black-Scholes Model and its Applications

A. S. Shinde et al.

INTERNATIONAL CONFERENCE ON MODELLING OPTIMIZATION AND COMPUTING (2012)

Add to Collection

Article Management

Competitive diffusion process of repurchased products in knowledgeable manufacturing

Hong-Sen Yan et al.

EUROPEAN JOURNAL OF OPERATIONAL RESEARCH (2011)

Add to Collection

Article Engineering, Multidisciplinary

Numerical methods for fractional partial differential equations with Riesz space fractional derivatives

Q. Yang et al.

APPLIED MATHEMATICAL MODELLING (2010)

Add to Collection

Article Computer Science, Interdisciplinary Applications

Finite difference/spectral approximations for the time-fractional diffusion equation

Yumin Lin et al.

JOURNAL OF COMPUTATIONAL PHYSICS (2007)

Add to Collection

Article Physics, Fluids & Plasmas

General solution of the diffusion equation with a nonlocal diffusive term and a linear force term

L. C. Malacarne et al.

PHYSICAL REVIEW E (2006)

Add to Collection

Article Chemistry, Analytical

Diffusion with general boundary conditions in electrochemical systems

C Criado et al.

JOURNAL OF ELECTROANALYTICAL CHEMISTRY (2000)

Add to Collection

© Peeref 2019-2024. All rights reserved.