A Finite Element Method With Singularity Reconstruction for Fractional Boundary Value Problems [PDF]
, 2015 We consider a two-point boundary value problem involving a Riemann-Liouville fractional derivative of order $\al\in (1,2)$ in the leading term on the unit interval $(0,1)$.
Jin, Bangti, Zhou, Zhi
core +5 more sources
Nonlinear Analysis: Modelling and Control, 2021 In this paper, we study the multi-point boundary value problems for a new kind of piecewise differential equations with left and right fractional derivatives and delay. In this system, the state variables satisfy the different equations in different time intervals, and they interact with each other through positive and negative delay.
Yuxin Zhang, Xiping Liu, Mei Jia
openaire +4 more sources
The discontinuous Galerkin method for fractional degenerate convection-diffusion equations [PDF]
, 2011 We propose and study discontinuous Galerkin methods for strongly degenerate convection-diffusion equations perturbed by a fractional diffusion (L\'evy) operator. We prove various stability estimates along with convergence results toward properly defined (
A. Dedner +30 more
core +1 more source
Stability Analysis of Fractional-Order Periodic Piecewise Nonlinear Systems
IEEE Access, 2023 This paper investigates the stability problem of fractional-order periodic piecewise nonlinear systems. As a preparation, the existence and uniqueness of solutions of the system are derived under the Lipschitz condition and expressed in an equivalent ...
Qingqing Li +4 more
doaj +1 more source
An Analysis of the Rayleigh-Stokes problem for a Generalized Second-Grade Fluid [PDF]
, 2015 We study the Rayleigh-Stokes problem for a generalized second-grade fluid which involves a Riemann-Liouville fractional derivative in time, and present an analysis of the problem in the continuous, space semidiscrete and fully discrete formulations.
Bazhlekova, Emilia +3 more
core +2 more sources
Collocation-Based Approximation for a Time-Fractional Sub-Diffusion Model
Fractal and Fractional, 2023 We consider the numerical solution of a one-dimensional time-fractional diffusion problem, where the order of the Caputo time derivative belongs to (0, 1). Using the technique of the method of lines, we first develop from the original problem a system of
Kaido Lätt +3 more
doaj +1 more source
On the Consistency of the Solutions of the Space Fractional Schr\"odinger Equation [PDF]
, 2012 Recently it was pointed out that the solutions found in literature for the space fractional Schr\"odinger equation in a piecewise manner are wrong, except the case with the delta potential.
El-Sayed A. M. A. +5 more
core +2 more sources
An algorithm for the numerical solution of two-sided space-fractional partial differential equations. [PDF]
, 2015 We introduce an algorithm for solving two-sided space-fractional partial differential equations. The space-fractional derivatives we consider here are left-handed and right-handed Riemann–Liouville fractional derivatives which are expressed by using ...
Ford, Neville J., Pal, Kamal, Yan, Yubin
core +1 more source
On the chaotic systems of attraction with fractional operators in a novel Lorenz system
Results in Control and OptimizationIn this research, a novel variant model of the classical Lorenz system is proposed by reformulating both the classical and fractional-order Lorenz systems through a new framework based on piecewise fractional derivatives.
Atul Kumar +4 more
doaj +1 more source
A robust study of a piecewise fractional order COVID-19 mathematical model
Alexandria Engineering Journal, 2022 In the current manuscript, we deal with the dynamics of a piecewise covid-19 mathematical model with quarantine class and vaccination using SEIQR epidemic model.
Anwar Zeb +3 more
doaj +1 more source