The use of fractional derivatives as a mathematical tool towards the development of more
robust mathematical models in certain areas of reservoir engineering is gaining attention in …

Thermal flooding is one of the most successful and widely used processes for heavy oil
recovery. The memory-based fluid flow model is effective in characterizing reservoir heat …

Constant-order derivative (COD) time fractional diffusion models have been successfully
employed to describe transport processes where the rate of diffusion or the diffusion …

The problem of flowing a Maxwell upper-convected fluid on a horizontal surface is
considered here in two conditions. One is the condition in which the plate is made of a …

In this paper, we consider the nonlinear $\Psi $-Hilfer impulsive fractional differential
equation. Our main objective is to derive the formula for the solution and examine the …

Reservoir simulator is widely known in the petroleum industry for analysing and predicting
the fluid flow behaviour through porous media. Conventional mathematical approach, which …

Reservoir simulation is used to demonstrate the dynamic physical processes of rocks and
fluid properties with high-order nonlinear equations. Currently, different types of simulation …

The reflection and transmission behaviors of elastic waves through a fluid-saturated double-
porosity interlayer are studied in present work. In order to simulate the interporosity flow …

This paper presents an efficient numerical method for the fractional-order generalization of
the stochastic Stokes–Darcy model, which finds application in various engineering …

The increasing applications of fractional calculus in simulating the anomalous transport
behavior in disordered and fractured heterogeneous porous media has grown rapidly over …