A novel spectral Galerkin/Petrov–Galerkin algorithm for the multi-dimensional space–time fractional advection–diffusion–reaction equations with nonsmooth solutions
The usual classical polynomials-based spectral Galerkin and Petrov–Galerkin methods
enjoy high-order accuracy for problems with smooth solutions. However, their accuracy and …
enjoy high-order accuracy for problems with smooth solutions. However, their accuracy and …
An easy to implement linearized numerical scheme for fractional reaction–diffusion equations with a prehistorical nonlinear source function
In this paper, we construct and analyze a linearized finite difference/Galerkin–Legendre
spectral scheme for the nonlinear Riesz-space and Caputo-time fractional reaction–diffusion …
spectral scheme for the nonlinear Riesz-space and Caputo-time fractional reaction–diffusion …
A spectral collocation method for solving the non-linear distributed-order fractional Bagley–Torvik differential equation
One of the issues in numerical solution analysis is the non-linear distributed-order fractional
Bagley–Torvik differential equation (DO-FBTE) with boundary and initial conditions. We …
Bagley–Torvik differential equation (DO-FBTE) with boundary and initial conditions. We …
Robust spectral treatment for time-fractional delay partial differential equations
MM Alsuyuti, EH Doha, BI Bayoumi… - … and Applied Mathematics, 2023 - Springer
Fractional delay differential equations (FDDEs) and time-fractional delay partial differential
equations (TFDPDEs) are the focus of the present research. The FDDEs is converted into a …
equations (TFDPDEs) are the focus of the present research. The FDDEs is converted into a …
High‐order finite difference/spectral‐Galerkin approximations for the nonlinear time–space fractional Ginzburg–Landau equation
This paper proposes and analyzes a high‐order difference/Galerkin spectral scheme for the
time–space fractional Ginzburg–Landau equation. For the time discretization, the L 2‐1 σ …
time–space fractional Ginzburg–Landau equation. For the time discretization, the L 2‐1 σ …
Efficient numerical simulations based on an explicit group approach for the time fractional advection–diffusion reaction equation
The time-fractional advection–diffusion reaction equation (TFADRE) is a fundamental
mathematical model because of its key role in describing various processes such as oil …
mathematical model because of its key role in describing various processes such as oil …
Modelling and numerical synchronization of chaotic system with fractional-order operator
KM Owolabi - International Journal of Nonlinear Sciences and …, 2022 - degruyter.com
Numerical solution of nonlinear chaotic fractional in space reaction–diffusion system is
considered in this paper on a large but finite spatial domain size x∈[0, L] for L≫ 0, x= x (x, y) …
considered in this paper on a large but finite spatial domain size x∈[0, L] for L≫ 0, x= x (x, y) …
A new method of solving the Riesz fractional advection–dispersion equation with nonsmooth solution
H Du, Z Chen - Applied Mathematics Letters, 2024 - Elsevier
The Riesz fractional advection–dispersion equation with weak singularities at boundaries is
solved. Our important contributions are to propose a new approach, construct successfully …
solved. Our important contributions are to propose a new approach, construct successfully …
Finite-difference and spectral-Galerkin methods in models, described by fractional partial differential equations with delay: Dissertation is Submitted for the Degree of …
AKO Ibrahim - 2023 - elar.urfu.ru
The relevance of the topic and the degree of its development. Models described by fractional
partial differential equations have developed into a potent instrument for mathematical …
partial differential equations have developed into a potent instrument for mathematical …