In this paper, we propose an effective numerical method to solve the one-and two-
dimensional time-fractional convection-diffusion equations based on the Caputo derivative …

The spectral collocation method based on the Vieta-Lucas polynomials is introduced here
for the flow of non-Newtonian Powell-Eyring fluid. The attentiveness is focused on some …

Fractional differential equations (FDEs) are utilized as a precise model for describing a wide
range of biological and physical processes, benefiting from the inherent symmetry feature in …

A higher-order finite difference method is developed to solve the variable coefficients
convection–diffusion singularly perturbed problems (SPPs) involving fractional-order time …

The reduced version of the fractional Laplace transform, called the v-Laplac transform, is
used in combination with the Adomian decomposition method to generate approximate …

This work employs newly shifted Lucas polynomials to approximate solutions to the time-
fractional Fitzhugh–Nagumo differential equation (TFFNDE) relevant to neuroscience. Novel …

This paper demonstrates, a numerical method to solve the one and two dimensional
Burgers' equation involving time fractional Atangana-Baleanu Caputo\(ABC\) derivative with …

The utilization of time-fractional PDEs in diverse fields within science and technology has
attracted significant interest from researchers. This paper presents a relatively new …

Here, we provide a new method to solve the time-fractional diffusion equation (TFDE)
following the spectral tau approach. Our proposed numerical solution is expressed in terms …

The utilization of time-fractional Burgers' equations is widespread, employed in modeling
various phenomena such as heat conduction, acoustic wave propagation, gas turbulence …