A review on variable-order fractional differential equations: mathematical foundations, physical models, numerical methods and applications

HG Sun, A Chang, Y Zhang, W Chen - Fractional Calculus and …, 2019 - degruyter.com
Variable-order (VO) fractional differential equations (FDEs) with a time (t), space (x) or other
variables dependent order have been successfully applied to investigate time and/or space …

Applications of variable-order fractional operators: a review

S Patnaik, JP Hollkamp… - Proceedings of the …, 2020 - royalsocietypublishing.org
Variable-order fractional operators were conceived and mathematically formalized only in
recent years. The possibility of formulating evolutionary governing equations has led to the …

Localized collocation schemes and their applications

Z Fu, Z Tang, Q **
VR Hosseini, E Shivanian, W Chen - Journal of Computational Physics, 2016 - Elsevier
The purpose of the current investigation is to determine numerical solution of time-fractional
diffusion-wave equation with dam** for Caputo's fractional derivative of order α (1< α≤ 2) …

A second-order difference scheme for the nonlinear time-fractional diffusion-wave equation with generalized memory kernel in the presence of time delay

AA Alikhanov, MS Asl, C Huang, A Khibiev - Journal of Computational and …, 2024 - Elsevier
This paper investigates a class of the time-fractional diffusion-wave equation (TFDWE),
which incorporates a fractional derivative in the Caputo sense of order α+ 1 where 0< α< 1 …

[HTML][HTML] A robust kernel-based solver for variable-order time fractional PDEs under 2D/3D irregular domains

ZJ Fu, S Reutskiy, HG Sun, J Ma, MA Khan - Applied Mathematics Letters, 2019 - Elsevier
This study presents a robust kernel-based collocation method (KBCM) for solving multi-term
variable-order time fractional partial differential equations (VOTFPDEs). In the proposed …

A wavelet approach for solving multi-term variable-order time fractional diffusion-wave equation

MH Heydari, Z Avazzadeh, MF Haromi - Applied Mathematics and …, 2019 - Elsevier
We firstly generalize a multi-term time fractional diffusion-wave equation to the multi-term
variable-order time fractional diffusion-wave equation (MV-TFD-E) by the concept of variable …

Stokes' first problem for heated flat plate with Atangana–Baleanu fractional derivative

N Sene - Chaos, Solitons & Fractals, 2018 - Elsevier
In this paper, we investigate on the exact solutions of the Stokes' first problem for
generalized second grade fluid with a new fractional derivative operator. The Riemann …