Novel applications of the magnetohydrodynamics couple stress fluid flows between two plates with fractal-fractional derivatives

In this work, we study the applications of recently introduced nonlocal differential operators with fractional order and fractal dimension referred as fractal-fractional differential operators in fluid dynamics. We consider the magnetohydrodynamics couple stress fluid flows between two parallel plates such that the lower plate is at rest while the upper plate is acting with constant velocity. For each operator, we demonstrate a comprehensive analysis containing numerical solutions and stability investigation.