Fractionized based rheological features of transient motion of Walter's B fluid in a rectangular oscillatory duct with cosine and sine oscillations

The area of fractional calculus, which incorporates fractional or noninteger order derivatives and integrals, has become one of the more effective fields. As compared to the traditional differentiation with derivatives of integer order, the branch of fractional calculus with derivatives of fractional order yields more powerful results in various disciplines including bioengineering, nonlinear dynamical systems, geophysics, etc. This study is organized to address the significance of powerful tool of fractional derivatives on the transient magnetized flow behavior of a Walter's B non-Newtonian fluid in a porous medium developed inside an oscillatory rectangular fluid. The flow behavior of fluid is examined in two dimensions by taking into account both cosine and sine oscillations. To observe the involvement of fractional derivative, an efficient Caputo fractional derivative is executed on the flow problem. The exact solution of the velocity field is manifested by executing double finite Fourier sine transform and Laplace transform techniques. The velocity distribution is also graphically explored corresponding to both types of oscillations and improved pertinent parameters. This fractional derivative based study manifests the result that the increasing values of the fractional parameter and fluid parameter yields an augmentation in the velocity field of the fluid.