The meshless approach for solving 2D variable-order time-fractional advection–diffusion equation arising in anomalous transport

An L1 type difference/Galerkin spectral scheme for variable-order time-fractional nonlinear diffusion–reaction equations with fixed delay

“…This emphasizes the evolutionary nature of the variable-order fractional calculus formalism, which indeed can play a critical role in the simulation of nonlinear dynamical models. Recognizing this untapped potential and unique capability of variable-order operators, the scientific community has been intensively investigating applications of variable-order fractional calculus to the modelling of physical and engineering systems [3][4][5][6][7][8][9].…”

A novel local Hermite radial basis function‐based differential quadrature method for solving two‐dimensional variable‐order time fractional advection–diffusion equation with Neumann boundary conditions

“…Nevertheless, the intrinsic complexity of fractional calculus, caused partially by non-local properties of fractional derivatives and integrals, makes it rather difficult to find efficient numerical methods in this field. Despite this fact, however, the literature exhibits a growing interest and improving achievements in numerical methods for fractional calculus in general [5][6][7][8][9][10][11][12][13][14].…”

New general integral transform via Atangana–Baleanu derivatives

“…However, researchers have come to realise that models constructed from fractional calculus can successfully represent real world problems and sometimes yield better results compared to models from the integer calculus. Some useful results from fractional calculus models appear in engineering, physics, biology and economics [1][2][3][4][5][6][7][8][9][10][11][12][13][14].…”